text large_stringlengths 99 26.4k | license large_stringclasses 1
value | metadata dict | uuid large_stringlengths 36 36 | split stringclasses 5
values |
|---|---|---|---|---|
Identify the antecedent of the following conditional proposition. Kurt will buy a new coat for his co-worker only if he saves money by avoiding shopping trips and the Los Angeles Rams win the Super Bowl.
A. Kurt saves money by avoiding shopping trips.
B. Kurt buys a new coat for his co-worker.
C. Kurt saves money by av... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 89d590ff-689b-4965-8392-eb5f66ff6c6f | Nemotron-Pretraining-Economics |
Select the best translation into predicate logic. Kathryn manages intense emotions with quiet evenings. (k: Kathryn; Ex: x is an intense emotion; Qy: y is a quiet evening; Mxyz: x manages y with z)
A. (∀x)(∀y)(Ex ∧ Qy → Mkxy)
B. (∃x)(∃y)(Ex ∧ Qy → Mkxy)
C. (∃x)(∃y)(Ex ∧ Qy ∧ Mkxy)
D. Mkekq
Answer: C | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | adc4da3d-a443-4ef6-8d82-3240a472c943 | Nemotron-Pretraining-Code-Concepts |
In a community group that includes Boris, Mason, and Paris, let the following predicates be defined:
- Vx: x volunteers at the hospital
- Sx: x is spontaneous
- Fxy: x is friends with y
- Ox: x organizes social events
Select the best English interpretation of the given proposition: (∃x)[(Vx ∧ Sx) ∧ (∀y)(Fxy → Oy)]
A. E... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | a814a53f-c1b2-436d-86b3-b82ff0f1794c | Nemotron-Pretraining-Formal-Logic |
Identify the antecedent of the following conditional proposition: Matias's board game prototype will be successful only if it features innovative design and benefits from market luck.
A. Matias's board game prototype features innovative design and benefits from market luck.
B. Matias's board game prototype benefits fro... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | e629887b-1525-4a69-9a57-54f4ba4e8e89 | Nemotron-Pretraining-Unconditional-Algorithmic |
Which of the following propositions is an immediate (one-step) consequence in Propositional Logic (PL) of the given premises?
D ⊃ (U ∨ V)
~(U ∨ V)
U ⊃ V
A. ~D
B. V
C. U
D. D
Answer: A | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 70153da9-1207-4e84-aa1d-53578fa55d4f | Nemotron-Pretraining-Unconditional-Algorithmic |
Let the following atomic propositions be defined in the context of three friends:
- H: Vici is on a spontaneous desert hike.
- E: Adriana is hosting a cultural event.
- S: Dilia is watching her favorite Spanish soap opera with café con leche.
Consider the propositional logic formula (H → ¬E) ∧ (E → S).
Which of the fol... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 4bee011f-96ea-492c-8f5b-a217c6d78a9c | Nemotron-Pretraining-Code-Concepts |
Select the best English interpretation of the given proposition, using the following translation key:
Ox: x is organized
Ax: x appreciates the arts
Cx: x plays chess
Oxy: x is older than y
(∃x)[(Ox • Ax) • (∃y)(Cy • Oxy)]
A. Every organized person who appreciates the arts is older than some chess player.
B. Some chess ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 7c9b0b9d-43ba-4303-83c0-616e4a24e05f | Nemotron-Pretraining-Economics |
Select the best English interpretation of the following argument expressed in predicate logic:
E(r) ⊃ ~S(j)
(∀x)T(x) ∨ (∃x)~M(x)
M(r)
∴ ~E(r)
Where E(x): x is an event planner, M(x): x is meticulous, T(x): x throws themed parties, S(x): x is spontaneous, r: Ruth, j: John
A. If Ruth is an event planner, then John is spo... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 9bd32f5e-3318-4fdb-b68f-6972855b0ccd | Nemotron-Pretraining-Unconditional-Algorithmic |
Quesion: Let the following atomic propositions be defined in the context of a community project led by Lyzette in Chicago:
- S: Lyzette schedules the team meeting.
- A: Eric is available to attend the meeting.
- P: Margaret presents the project update.
Consider the propositional logic formula (S → ¬A) ∧ (A → P).
Which ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | c373de68-f704-4853-ae13-1747f05380a9 | Nemotron-Pretraining-Formal-Logic |
Select the best translation into predicate logic: Some cautious people are curious.
A. (∃x)(Cx ∧ Kx)
B. (∃x)(Cx ∨ Kx)
C. (∃x)(Cx ⊃ Kx)
D. (∀x)(Cx ∧ Kx)
Answer: A | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | c939538c-48d3-45a6-8978-bc16134bf722 | Nemotron-Pretraining-Multiple-Choice |
Quesion: Select the best English interpretation of the given argument in predicate logic.
(∀x)[(Px • Sx) ⊃ Ux]
(∃x)(Px • ~Ux)
∴ (∃x)(Px • ~Sx)
Where Px: x is a gardener, Sx: x is structured in their gardening approach, Ux: x experiences unexpected blooms
Options:
A. All gardeners who are structured experience unexpecte... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | b9879c96-afbc-4337-acc1-3de6e2189d10 | Nemotron-Pretraining-Economics |
Quesion: Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
(W ∧ Q) ⊃ B
R ∨ ~B
~R / ∴ ~W
Options:
A. Vali... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 99483d3f-b7a7-4dfc-a4b3-dbb700aa2c8a | Nemotron-Pretraining-Economics |
Select the best English interpretation of the given argument in predicate logic.
(∀x)[(Sx ∧ Tx) ⊃ Bx]
(∃x)(Sx ∧ ~Bx)
∴ (∃x)(Sx ∧ ~Tx)
Where Sx: x is a senior citizen, Tx: x is a teacher, Bx: x bakes whoopie pies
A. All senior teachers bake whoopie pies. Some seniors do not bake whoopie pies. Therefore, some seniors are... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | e638e6eb-9c15-4c99-adcb-e1e93089f255 | Nemotron-Pretraining-Multiple-Choice |
In the context of Savannah's Book Nook, consider the following atomic propositions:
- S: The author submits the final draft.
- P: The publisher prints the book.
- C: The contract is signed.
Select the best English interpretation of the propositional logic formula: (S → P) ∧ (¬C → ¬P)
A. The author submitting the final ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 728e6119-835f-492d-b490-37dfa2b54d17 | Nemotron-Pretraining-Multiple-Choice |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
Premises:
1. (O ≡ H) ∧ A
2. ~O ∨ H
3. C
4. M ≡ M
5. N ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | ac6605f3-08fe-4bf1-93c5-9f9d1166c42c | Nemotron-Pretraining-Unconditional-Algorithmic |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
(R ≡ O) ⊃ M
~M
/ ∴ R
A. Valid
B. Invalid. Counterexamp... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 4069d847-59af-468b-a372-5593d00d4745 | Nemotron-Pretraining-Economics |
Select the best translation into predicate logic. Some educators inspire all students they teach. (Ex: x is an educator; Sy: y is a student; Txy: x teaches y; Ixy: x inspires y)
A. (∀x)(Ex → (∀y)((Sy ∧ Txy) → Ixy))
B. (∀x)(Ex → (∃y)(Sy ∧ Txy ∧ Ixy))
C. (∃x)(Ex ∧ (∀y)((Sy ∧ Txy) → Ixy))
D. (∃x)(Ex → (∀y)((Sy ∧ Txy) → Ix... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 953289f0-97d2-4ab6-8e0d-709bc4494693 | Nemotron-Pretraining-Unconditional-Algorithmic |
Quesion: Use indirect truth tables to determine whether the following set of propositions is consistent. If the set is consistent, choose an option which presents a consistent valuation. (There may be other consistent valuations.)
(B ∨ O) ⊃ T
T ≡ (O ∨ ¬B)
B
¬T
Options:
A. Inconsistent
B. Consistent. Consistent valuatio... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 82c114aa-a916-4b63-9eca-66b89aaba5ce | Nemotron-Pretraining-Multiple-Choice |
Select the best translation into predicate logic: Ran loves some old cars.
A. ∃x (C(x) ∧ O(x) ∧ L(r,x))
B. ∃x (C(x) ⊃ (O(x) ∧ L(r,x)))
C. ∀x (C(x) ∧ O(x) ∧ L(r,x))
D. C(x) ∧ O(x) ∧ L(r,x)
Answer: A | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 62c4ddaa-25a5-4198-af3f-28c4a29cea7a | Nemotron-Pretraining-Formal-Logic |
Select the best English interpretation of the following argument expressed in predicate logic:
(∀x)[ (C(x) ∧ Q(x)) ⊃ (E(x) ∨ M(x)) ]
C(k) ∧ Q(k) ∧ ¬E(k)
∴ M(k)
Where:
C(x): x is a creature of habit
Q(x): x finds comfort in quiet environments
E(x): x enjoys embroidery
M(x): x observes Mole Sundays
k: Katiria
A. If a per... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 1b0ff035-bb71-45ec-9a18-2d336d6c59b0 | Nemotron-Pretraining-Economics |
Which of the following propositions is an immediate (one-step) consequence in Propositional Logic (PL) of the given premises?
P ⊃ (T ∨ Z)
(T ∨ Z) ⊃ (D ∧ F)
~(D ∧ F)
A. T ⊃ Z
B. ~P
C. D ∨ F
D. ~(T ∨ Z)
Answer: D | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 8ab4c783-382e-4b39-82e3-f861dc4014e2 | Nemotron-Pretraining-Code-Concepts |
Select the best English interpretation of the given proposition, using the following translation key: Qx: x is a puzzle Lx: x is a logic puzzle Sx: x is solved by Doris Tx: x is solved by Jane Hxy: x is harder than y (∃x)[(Qx • Lx) • (Sx • (∃y)(Qy • Ly • Hxy • Ty))]
A. Doris solved some logic puzzle that is harder than... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | d744bdd8-38c6-4b1f-bf0f-737c6d60db72 | Nemotron-Pretraining-Code-Concepts |
Quesion: Select the best translation into predicate logic. Qun tunes a guqin string. (q: Qun; Sx: x is a string; Gx: x is a guqin; Txyz: x tunes y of z)
Options:
A. T(q, s, g)
B. ∃s (Ss ∧ T(q, s))
C. ∃s ∃g (Ss ∧ Gg → T(q, s, g))
D. ∃s ∃g (Ss ∧ Gg ∧ T(q, s, g))
Answer: We are asked to translate the sentence "Qun tunes a... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 3b82ffc9-cb6f-4786-b124-9b2d58c3954b | Nemotron-Pretraining-Formal-Logic |
Quesion: In the context of Lonnie and Antoinette's community activities, consider the following propositional logic formula, where:
- G: Lonnie is tending his garden.
- T: Lonnie is teaching at the community center.
- A: Antoinette is hosting a community gathering.
- M: Antoinette is preparing a soulful meal.
Formula: ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 847b9d6e-5d66-4561-8fa0-0f9e879fe237 | Nemotron-Pretraining-Multiple-Choice |
Select the best translation into predicate logic: Luis helps Leslie.
A. Hs
B. Hsl
C. Hls
D. Hl
Answer: C | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | b8ef05cd-aac8-49be-88b2-2c1f058f73bd | Nemotron-Pretraining-Code-Concepts |
Let the following atomic propositions be defined in the context of a community arts collaboration:
- L: Lewis creates a landscape sketch inspired by the changing seasons of Minnesota.
- I: Sudeep incorporates innovative elements into his carpentry projects.
- K: Karla integrates carpentry concepts into her lesson plans... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 46174f35-1ccf-4fbe-b879-4f52a6289c7f | Nemotron-Pretraining-Economics |
Select the best translation into predicate logic. Jose Cristofer shares some art with all his guests. (Ax: x is art by Jose Cristofer; Gy: y is a guest of Jose Cristofer; Sxyz: x shares y with z; j: Jose Cristofer)
A. (∀x)(Ax → (∃y)(Gy ∧ Sj x y))
B. (∃x)(Ax → (∀y)(Gy → Sj x y))
C. (∀y)(Gy → (∃x)(Ax ∧ Sj x y))
D. (∃x)(A... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 04cd63db-906c-4ce6-8d36-13ccb38fd2bc | Nemotron-Pretraining-Code-Concepts |
Select the best English interpretation of the following argument expressed in predicate logic:
Vw ⊃ Ow
(∀x)(Jx ⊃ Cx) ∨ (∃x)¬Dx
Dg
∴ ¬Vw
Where Vx: x volunteers, Ox: x overcommits, Jx: x makes traditional jewelry, Cx: x uses CAD software, Dx: x worries about details, w: William, g: Govindbhai.
A. If William volunteers, h... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 9f08c3d3-e9f6-482c-be23-064fd457da8e | Nemotron-Pretraining-Unconditional-Algorithmic |
Which of the given formulas of PL is the best symbolization of the following sentence?
Either drinking Earl Grey tea is a necessary condition for Sandra to feel comfortable, or Michel hosts dinner debates if and only if his friends are available.
A. (E ⊃ C) ∨ (H ≡ F)
B. (C ⊃ E) ∨ (H ≡ F)
C. (E ⊃ C) ∨ (F ⊃ H)
D. (C ⊃ E)... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | a9c93dc2-5ee6-48f6-8499-9dcfe7262a67 | Nemotron-Pretraining-Code-Concepts |
Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
(P ≡ E) ⊃ (W ∧ S)
~S
E ⊃ P
/ W
A. Invalid. Counterexample when P is true, E is false, W is false, S is false
B. Vali... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | e62bf138-dca0-4c1a-9a13-1bbd2cb9ecdb | Nemotron-Pretraining-Unconditional-Algorithmic |
Quesion: Select the best English interpretation of the given argument in predicate logic.
(∀x)[(Hx • Tx) ⊃ Bx]
(∃x)(Hx • ~Bx)
∴ (∃x)(Hx • ~Tx)
Where Hx: x is a hiker, Tx: x trails new paths, Bx: x balances structure and adaptability.
Options:
A. If a hiker trails new paths, they balance structure and adaptability. Some... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | b4c53114-a649-4261-8326-9f3d22168c5c | Nemotron-Pretraining-Economics |
Which of the given formulas of PL is the best symbolization of the following sentence?
Either Micah practices daily is a necessary condition for him to win the chess tournament, or Ying creates a balanced design if but only if she feels inspired.
A. (M ⊃ P) ∨ (I ⊃ D)
B. (P ⊃ M) ∨ (D ⊃ I)
C. (M ⊃ P) ∨ (D ≡ I)
D. (P ⊃ M)... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | b86e0cdb-fe72-478b-a98e-029e3eeb3310 | Nemotron-Pretraining-Economics |
Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
\((F \land K) \equiv O\)
\(B \lor E\)
\(O \supset (B \land E)\)
Therefore, \(F \supset E\)
A. Invalid. Counterexampl... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | d32a3bca-5a52-40f9-b8e7-e40f9a1faed1 | Nemotron-Pretraining-Economics |
Which of the given formulas of PL is the best symbolization of the following sentence?
Either a city permit is necessary for Nkrumah's community art event to occur, or Fawn will host a workshop only if Christian helps with the setup.
A. (E ⊃ P) ∨ (F ⊃ H)
B. (E ⊃ P) ∨ (H ⊃ F)
C. (P ⊃ E) ∨ (F ⊃ H)
D. (P ⊃ E) ∨ (H ⊃ F)
An... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 5d165186-5048-4bd2-b131-f50f3c3707bf | Nemotron-Pretraining-Multiple-Choice |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
(G ≡ F) ⊃ (L ∧ X)
~(X ∨ Z)
F ≡ L / ∴ ~G
A. Valid
B. In... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 720fd1e6-b241-4eda-953a-4da45a426310 | Nemotron-Pretraining-Formal-Logic |
Consider the propositional logic formula (C → ¬H) ∧ (H → P), with the following atomic propositions defined in the context of planning a Chuseok celebration:
- C: Crystal is attending the dinner.
- H: Chaoying is cooking the meal.
- P: Petrina has made the guest list.
Which of the following English statements best expr... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | adea27d8-0b03-4305-9b71-cbaa95f8f657 | Nemotron-Pretraining-Formal-Logic |
Use indirect truth tables to determine whether the following set of propositions is consistent. If the set is consistent, choose an option which presents a consistent valuation. (There may be other consistent valuations.)
(Q ∨ N) ⊃ K
E ⊃ (Z ∧ D)
(K ∨ E) ≡ (Q ∧ Z)
∼D ⊃ (N ∨ K)
A. Consistent. Consistent valuation when Q ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | d51ffeb0-e1a7-444a-a579-0d41ce34737a | Nemotron-Pretraining-Multiple-Choice |
Which of the given formulas of PL is the best symbolization of the following sentence?
Either solving mysteries is a necessary condition for Brannon to play guitar, or Gerrie reads every day if but only if she preserves history.
A. (M ⊃ G) ∨ (R ⊃ H)
B. (G ⊃ M) ∨ (R ⊃ H)
C. (G ⊃ M) ∨ (R ≡ H)
D. (M ⊃ G) ∨ (R ≡ H)
Answer:... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | ddfa5d75-c79b-4fc9-83cf-e552c1c6c8f4 | Nemotron-Pretraining-Multiple-Choice |
Select the best translation into predicate logic. Carl appreciates all of Jamalia's books. (c: Carl; j: Jamalia; Bx: x is a book; Oxy: x owns y; Axy: x appreciates y)
A. (∀y)(Ojy → Acy)
B. (∀y)((By ∧ Ojy) → Acy)
C. (∀y)(By → Ojy) → (∀y)(By → Acy)
D. (∃y)(By ∧ Ojy ∧ Acy)
Answer: B | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 072b5c41-75ce-42fe-a880-df5abc447623 | Nemotron-Pretraining-Code-Concepts |
Quesion: Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
(P ∧ T) ⊃ ~F
F ∨ T
~P
U ∨ ~U / ∴ T
Options:
A... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 8c0c9cff-eaaf-46b2-8768-9d7848b534ba | Nemotron-Pretraining-Formal-Logic |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
U ∨ I
J ⊃ Y
~(U ∧ Y) / ∴ ~(I ∨ J)
A. Valid
B. Invalid.... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | c48faa3d-438e-49c5-a2df-e60439fd6767 | Nemotron-Pretraining-Economics |
Quesion: Select the best translation into predicate logic: All of Ronald's routines involve coffee.
Options:
A. (∀x)(Rx ⊃ Cx)
B. (∀x)(Cx ⊃ Rx)
C. (∀x)(Rx ∧ Cx)
D. (∃x)(Rx ⊃ Cx)
Answer: Step 1: Analyze the statement "All of Ronald's routines involve coffee." This means every routine that Ronald has must include coffee. ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 8847214e-27ca-4bb9-b809-79e800b867be | Nemotron-Pretraining-Economics |
Which of the given formulas of PL is the best symbolization of the following sentence?
Either Christine carries a classic novel if and only if she is not struggling to keep her desk organized, or Jonathan sets up an ofrenda only if he tends to his garden.
A. (C ≡ ~D) ∧ (O ⊃ G)
B. (C ≡ D) ∨ (O ⊃ G)
C. (C ≡ ~D) ∨ (O ⊃ G)... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | bc4d32ff-7d0f-4d3b-b5ab-20bb0d35fa91 | Nemotron-Pretraining-Multiple-Choice |
Quesion: Select the best English interpretation of the given argument in predicate logic.
Fg ⊃ (Sg ∧ Ag)
(∀x)(Hx → Bx) ∨ (∃x)¬Sx
Sc
¬Bc
∴ ¬Fg
Where Fx: x is a flight attendant, Sx: x is a social butterfly, Ax: x is adaptable, Bx: x balances multiple projects, Hx: x is a history buff, g: Grace, c: Carolina
Options:
A. I... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | e504eaf4-ed33-42e5-8f7a-80b800e43305 | Nemotron-Pretraining-Economics |
Select the best English interpretation of the given proposition, using the following translation key:
Dx: x is a dish prepared by Dorothy.
Sx: x is savory.
Tx: x is sweet.
Gx: x is a guest.
Exy: guest x enjoys dish y.
Proposition: (∃x)[ (Dx • Sx) • (∃y)[ (Dy • Ty) • (∃z)( Gz • Ezx • ¬Ezy ) ] ]
A. Every guest enjoys som... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | e37b137c-16cb-4b4a-bfc1-79f6e851b746 | Nemotron-Pretraining-Unconditional-Algorithmic |
Consider the following atomic propositions in the context of a medical diagnosis system:
- F: The patient has a fever
- C: The patient has a cough
- T: The patient tested positive for the virus
- I: The patient requires isolation
Select the best English interpretation of the propositional logic formula:
**(F → (C ∨ T))... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 4a727480-f743-48b9-bc17-77d9c3f452db | Nemotron-Pretraining-Unconditional-Algorithmic |
Identify the antecedent of the following conditional proposition. Jeanette, a numbers whiz with a soulful side, balances ledgers with paintbrushes at the store. While humming a tune from a recent Milwaukee Bucks concert, she considered that if the atmospheric water generator is functioning, then she can safely ignore t... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 27f12839-692b-4d75-bc1f-e012df5caaaf | Nemotron-Pretraining-Formal-Logic |
Use indirect truth tables to determine whether the following set of propositions is consistent. If the set is consistent, choose an option with a consistent valuation. (There may be other consistent valuations.)
(T ∨ G) ⊃ R
R ⊃ (Y ∨ G)
(T ∨ Y) ≡ ∼G
G ∨ ∼Y
A. Consistent. Consistent valuation when T is false, G is false,... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 0feb5574-50fb-493e-9736-a3844eac65a1 | Nemotron-Pretraining-Formal-Logic |
Which of the given formulas of PL is the best symbolization of the following sentence?
Akhter will organize a poetry workshop only if Gary attends, and Andrew will join the event if and only if it is on a weekend.
A. (G ⊃ O) ∧ (J ≡ W)
B. (O ⊃ G) ∧ (J ≡ W)
C. (O ⊃ G) ∧ (J ⊃ W)
D. (O ≡ G) ∧ (J ≡ W)
Answer: B | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 99224e98-c482-4eb9-8cee-1765f57c6f10 | Nemotron-Pretraining-Economics |
Let the following atomic propositions be defined in the context of a community cultural event:
- P: Anna is participating in the art competition.
- Q: Consuelo is sharing her cultural story.
- R: Jose is sacrificing sleep to ensure everything is perfect.
- S: The community event is a success.
Consider the propositional... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | b41b33c4-113b-4077-850d-c6c5172c29ec | Nemotron-Pretraining-Formal-Logic |
Select the best English interpretation of the given argument in predicate logic.
(∀x)[(Sx • Cx) ⊃ Px]
(∃x)(Sx • ~Px)
∴ (∃x)(Sx • ~Cx)
Where Sx: x is a student in Joan's creative writing class, Cx: x completes the weekly creative assignment, Px: x passes the course
A. If a student in Joan's class passes the course, they... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | bd56b584-53a9-423f-b0a0-7d912e35fbae | Nemotron-Pretraining-Code-Concepts |
Quesion: Select the best translation into predicate logic. Some mentors value harmony with all colleagues. (Mx: x is a mentor; Cx: x is a colleague; Hxy: x values harmony with y)
Options:
A. (∃x)(Mx → (∀y)(Cy → Hxy))
B. (∀x)(Mx → (∃y)(Cy ∧ Hxy))
C. (∃x)(Mx ∧ (∀y)(Cy → Hxy))
D. (∃x)(∀y)((Mx ∧ Cy) → Hxy))
Answer: ### Ste... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 095e9c08-5029-4fd4-9571-21c3f8006d0a | Nemotron-Pretraining-Economics |
Select the best translation into predicate logic: Todd does not own any car.
A. ∃x(Cx ∧ ¬Otx)
B. ∀x(Cx → ¬Otx)
C. ¬∀x(Cx → Otx)
D. ∀x(Cx → Otx)
Answer: B | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 7ca13030-1e13-4bc1-b837-95cfd8e17116 | Nemotron-Pretraining-Formal-Logic |
Select the best English interpretation of the following argument expressed in predicate logic:
R h ⊃ ~J p
(∀x) M x ∨ (∃x) ~G x
J p
∴ ¬R h
Where R x: x is retired, J x: x loves jazz, M x: x is musical, G x: x is a gardener.
A. If Heidi is retired, then Paulette does not love jazz. Either everyone is musical or someone i... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | f275563f-80ce-4410-a38b-155887eae20b | Nemotron-Pretraining-Formal-Logic |
Select the best translation into predicate logic: Some young artists write short stories.
A. ∃x (Yx ⊃ Wx)
B. ∀x (Yx ⊃ Wx)
C. ∃x Yx ∧ ∃x Wx
D. ∃x (Yx ∧ Wx)
Answer: D | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 41cb0455-6005-468f-a86d-5db37d8761ce | Nemotron-Pretraining-Code-Concepts |
Which of the following propositions is an immediate (one-step) consequence in Propositional Logic (PL) of the given premises?
J ⊃ (D ∨ M)
(D ∨ M) ⊃ Z
~Z
A. ~(D ∨ M)
B. Z
C. ~D
D. ~J
Answer: A | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | c41c12d8-ef18-4682-a467-9b2539c48421 | Nemotron-Pretraining-Code-Concepts |
Select the best translation into predicate logic. Michael introduces some artists to his neighbors. (Ax: x is an artist; Nx: x is a neighbor of Michael; Ixyz: x introduces y to z; m: Michael)
A. (∃y)(∃z)(Ay → (Nz → I m y z))
B. Iman
C. (∃y)(∃z)(Ay ∧ Nz ∧ I m y z)
D. (∀y)(∀z)(Ay ∧ Nz → I m y z)
Answer: C | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 96305d05-e39f-4f72-819b-96e620938eec | Nemotron-Pretraining-Formal-Logic |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
Premises:
1. (W ⊃ G) ∨ L
2. ~H ⊃ ~W
3. L ≡ H
Conclusio... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | cc34cb31-c79d-47ee-a7d1-87914463206a | Nemotron-Pretraining-Multiple-Choice |
Identify the antecedent of the following conditional proposition. Daniel, a retiree who balances curiosity with practicality much like the Blue Ridge Mountains he calls home, has deployed a digital twin to monitor a historic building overlooking a deep canyon. He asserts that if the digital twin integrates real-time da... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 01c63b79-f85b-49be-afcc-05419b080270 | Nemotron-Pretraining-Unconditional-Algorithmic |
Select the best translation into predicate logic. Alberto is a social worker who plays the guitar. (a: Alberto; Sx: x is a social worker; Gx: x is a guitar; Play(x,y): x plays y)
A. S(a) ∧ (∀y)(Gy → Play(a,y))
B. S(a) ∧ (∃y)(Gy → Play(a,y))
C. S(a) ∧ (∃y)(Gy ∧ Play(a,y))
D. S(a) ∧ Play(a,g)
Answer: C | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | ced8a613-9048-4ce8-931b-14e958846a28 | Nemotron-Pretraining-Code-Concepts |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
D ⊃ M
M ⊃ N
N ≡ B
D
∴ Z ≡ B
A. Invalid. Counterexample... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | f6363602-e760-436e-b4eb-ba78f6bc936f | Nemotron-Pretraining-Formal-Logic |
Select the best English interpretation of the following argument expressed in predicate logic:
(∀x)(Rx → (Tx ∨ ¬Vx))
Rr
Vr
∴ Tr
Where Rx: x is retired, Tx: x is traditional, Vx: x is a volunteer, and r represents Rida.
A. Every retired person is traditional or not a volunteer. Rida is retired. Rida is not a volunteer. ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | c9553794-04e4-49c0-9513-61f47551a747 | Nemotron-Pretraining-Multiple-Choice |
Select the best translation into predicate logic. Thanh Ann tells every story about local history to Wilson. (ta: Thanh Ann; w: Wilson; Sx: x is a story; Hx: x is about local history; Txyz: x tells y to z)
A. (∀y)((Sy → Hy) → T(ta,y,w))
B. (∃y)((Sy ∧ Hy) ∧ T(ta,y,w))
C. (∀y)((Sy ∧ Hy) → T(ta,y,w))
D. (∀y)(T(ta,y,w) → (... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 05d1fd79-d067-4e45-81bb-51ca1b5bc4a8 | Nemotron-Pretraining-Multiple-Choice |
Select the best translation into predicate logic: Joyce attends every traditional festival.
A. ∀x (Tx → Ax)
B. ∀x (Ax → Tx)
C. ∀x (Tx ∧ Ax)
D. ∃x (Tx → Ax)
Answer: A | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 3e35f786-4cc8-4c50-a9f6-d44c1e7b4619 | Nemotron-Pretraining-Multiple-Choice |
Which of the given formulas of PL is the best symbolization of the following sentence?
Either Dot plays bridge only if she tends her garden, or Fabio works in his garage if but only if Van James is pruning roses.
A. (G ⊃ B) ∨ (W ≡ P)
B. (B ⊃ G) ∨ (W ≡ P)
C. (G ⊃ B) ∨ (P ⊃ W)
D. (B ⊃ G) ∨ (W ⊃ P)
Answer: B | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 675be40c-8aaf-47ce-8ce7-3d534fa1c9c7 | Nemotron-Pretraining-Economics |
Quesion: Which of the following propositions is an immediate (one-step) consequence in Propositional Logic (PL) of the given premises?
(M ≡ R) ⊃ N
~N
M ⊃ R
Options:
A. M ≡ R
B. N
C. ~(M ≡ R)
D. R
Answer: We are given the following premises in propositional logic (PL):
1. $ (M \equiv R) \supset N $
2. $ \neg N $
3. $ M... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | a0ac614d-ed6e-40e3-9892-ce92e27ab721 | Nemotron-Pretraining-Unconditional-Algorithmic |
Select the best translation into predicate logic. Violet improves some established processes. (v: Violet; Px: x is a process; Ex: x is established; Ixy: x improves y)
A. (∃x)(Px ∧ I v x)
B. (∃x)(Px ∧ Ex ∧ I v x)
C. (∀x)(Px ∧ Ex → I v x)
D. (∃x)(Px → (Ex ∧ I v x))
Answer: B | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 76327da0-38e5-41f4-8695-585668b06c5e | Nemotron-Pretraining-Economics |
Select the best translation into predicate logic. Some storytellers tell stories to children. (Sx: x is a storyteller; Ty: y is a story; Cz: z is a child; Txyz: x tells y to z)
A. (∃x)(Sx → (∃y)(∃z)(Ty ∧ Cz ∧ Txyz))
B. (∃x)(Sx ∧ (∃y)(∃z)(Ty ∧ Cz ∧ Txyz))
C. (∃x)(Sx ∧ Txsc)
D. (∀x)(Sx → (∀y)(∀z)(Ty ∧ Cz → Txyz))
Answer:... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 4391f8db-ccaf-4e59-afe0-f2cac7454392 | Nemotron-Pretraining-Code-Concepts |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
J ⊃ (B ∨ M)
~K ≡ M
B / ∴ J ⊃ K
A. Invalid. Counterexam... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | b18197ee-90ed-42b3-b5ef-2e3ef25cc89a | Nemotron-Pretraining-Economics |
Select the best translation into predicate logic: McKayla helps every neighbor.
A. ∀x (Nx ⊃ Hxm)
B. ∀x (Hmx ⊃ Nx)
C. ∀x (Nx ⊃ Hmx)
D. ∃x (Nx ∧ Hmx)
Answer: C | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | b5359399-4baa-43aa-8938-a9d481544f6f | Nemotron-Pretraining-Unconditional-Algorithmic |
Select the best English interpretation of the given argument in predicate logic.
(∀x)[Sx ⊃ (Cx ∨ Ex)]
Sl ∧ ~El
∴ Cl
Where Sx: x is a security expert, Cx: x is certified in cybersecurity, Ex: x has extensive experience
A. All security experts are both certified in cybersecurity and have extensive experience. Luis is a s... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 26c6f4a8-ca00-4479-8d5c-0ef6382bc416 | Nemotron-Pretraining-Unconditional-Algorithmic |
Select the best translation into predicate logic. Kuran sketches an innovative idea for Dontrell. (k: Kuran; d: Dontrell; Ix: x is an innovative idea; Sxyz: x sketches y for z)
A. (∀y)(Iy → Sk y d)
B. (∃y)(Iy ∧ Sk y d)
C. (∃x)(∃y)(Ix ∧ Sxy d)
D. (∃y)(Iy ∧ Sk d y)
Answer: B | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | d7c47658-e8e9-49b6-a4f3-7493413b874b | Nemotron-Pretraining-Unconditional-Algorithmic |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
(E ≡ U) ⊃ Q
E ∨ ~Q
U / ∴ Q
A. Invalid. Counterexample ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 0de5bbc8-d3a2-4950-8cde-1d09cf4404af | Nemotron-Pretraining-Unconditional-Algorithmic |
Which of the given formulas of PL is the best symbolization of the following sentence?
If Joseph is not careful, he loses his magnifying glasses, but he is careful only if he is not distracted.
A. (~C ⊃ L) ∨ (C ⊃ ~D)
B. (C ⊃ L) ∧ (~D ⊃ C)
C. (L ⊃ ~C) ∧ (~D ⊃ C)
D. (~C ⊃ L) ∧ (C ⊃ ~D)
Answer: D | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 6f010a74-d8cc-44f5-a408-7a917b68d41a | Nemotron-Pretraining-Economics |
Select the best translation into predicate logic. Otha hikes some trails alone. (o: Otha; Tx: x is a trail; Hxy: x hikes y alone)
A. (∃y)(H(o,y))
B. (∃y)(Ty ∧ H(y,o))
C. (∀y)(Ty → H(o,y))
D. (∃y)(Ty ∧ H(o,y))
Answer: D | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | b4ff4e2d-9d66-4bd6-8881-44fc44600869 | Nemotron-Pretraining-Multiple-Choice |
Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
I ⊃ (L ∨ Q)
~Q ≡ I
L / ∴ I
A. Invalid. Counterexample ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | f587b2f7-1315-4c12-91a6-10b665ce4fac | Nemotron-Pretraining-Formal-Logic |
Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
(L ∨ A) ≡ C
~C ∨ D
D ⊃ ~L
/ ~A
A. Invalid. Counterexample when L is false, A is false, C is false, D is false
B. Val... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 14ee81b6-5304-47db-9551-7ea72f0c3130 | Nemotron-Pretraining-Economics |
Which of the given formulas of PL is the best symbolization of the following sentence?
Marilyn will host a spontaneous gathering only if she has no work obligations, and she plays the piano unless it is raining.
A. (M ⊃ ~W) ∧ (~R ⊃ P)
B. (M ⊃ W) ∧ (R ⊃ P)
C. (M ⊃ ~W) ∨ (R ⊃ P)
D. (~W ⊃ M) ∧ (P ⊃ ~R)
Answer: A | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | edc8ed47-633f-477a-b87c-b5dfcfd41d16 | Nemotron-Pretraining-Formal-Logic |
Select the best translation into predicate logic. Douglas quotes some film line to all partygoers. (Px: x is a partygoer; Fx: x is a film line; Qxyz: x quotes y to z; d: Douglas)
A. (∀z)(∃y)(Fy ∧ Qd y z)
B. (∃y)(∀z)(Pz → Qd y z)
C. (∀z)(Pz → (∃y)(Fy ∧ Qd y z))
D. (∃y)(Fy ∧ (∀z)(Pz → Qd y z))
Answer: D | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | b1408fb2-e8b0-4244-9302-5c551b6b4e53 | Nemotron-Pretraining-Unconditional-Algorithmic |
Which of the given formulas of PL is the best symbolization of the following sentence?
Stephen will attend the potluck only if Luis is not working late and Michelle brings food.
A. A ⊃ (~W ∧ F)
B. A ⊃ (W ∧ F)
C. (~W ∧ F) ⊃ A
D. A ≡ (~W ∧ F)
Answer: A | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | f12c5176-fecc-47fa-93ea-eb59b28b38ba | Nemotron-Pretraining-Multiple-Choice |
Quesion: Identify the antecedent of the following conditional proposition. If Phyllis uses her toolbelt to repair the bicycle in the maker space, then the virtual avatar will initiate a music sequence for the stranger.
Options:
A. The virtual avatar will initiate a music sequence for the stranger.
B. Phyllis uses her t... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | cea168c0-b393-461d-95ce-4be60cbf27f6 | Nemotron-Pretraining-Code-Concepts |
Quesion: Identify the antecedent of the following conditional proposition: If the autonomous drone swarm successfully monitors the fire and Adelaida approves the safety protocol, then the fruit harvest will be protected from damage.
Options:
A. The autonomous drone swarm successfully monitors the fire.
B. Adelaida appr... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 82af0732-5f46-449e-b014-0e6e36f8b069 | Nemotron-Pretraining-Formal-Logic |
Select the best translation into predicate logic: Della is a social butterfly but not reliable.
A. Sd ∧ Rd
B. Sd ∨ ¬Rd
C. Sd ∧ ¬Rd
D. ¬(Sd ∧ Rd)
Answer: C | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 985e646d-a122-4b1b-b444-c18a1081eefa | Nemotron-Pretraining-Unconditional-Algorithmic |
Quesion: Which of the given formulas of PL is the best symbolization of the following sentence?
Charles will fix the old watch only if Don provides the tools, but Romeo will join the clean-up if and only if Charles shares a story from Twentynine Palms.
Options:
A. (C ⊃ D) ∨ (R ≡ S)
B. (D ⊃ C) ∧ (R ≡ S)
C. (C ⊃ D) ∧ (R ... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 315432dc-0ce3-47f8-ba5b-eb721bd6a6e3 | Nemotron-Pretraining-Formal-Logic |
Select the best translation into predicate logic. Some of Vicente's routines are more practical than all of Gregory's hobbies. (v: Vicente; g: Gregory; Rx: x is a routine; Hx: x is a hobby; Bxy: x belongs to y; Pxy: x is more practical than y)
A. ∃x (Rx ∧ Bxv ∧ ∀y ( (Hy ∧ Byg) → Pxy ) )
B. ∀y ∃x (Rx ∧ Bxv ∧ (Hy ∧ Byg →... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 9b894ca6-ad1b-4d3a-bb97-dcf86ceb0479 | Nemotron-Pretraining-Economics |
Select the best translation into predicate logic: Not every retired businessman is competitive.
A. (∃x)(Rx ∧ ¬Cx)
B. (∀x)(Rx ⊃ Cx)
C. (∃x)(Rx ⊃ ¬Cx)
D. (∀x)(Rx ⊃ ¬Cx)
Answer: A | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 55a2945f-3865-4f59-8624-7d6d94352ae1 | Nemotron-Pretraining-Unconditional-Algorithmic |
Select the best translation into predicate logic. All nurturers like some flowers. (Nx: x is a nurturer; Fx: x is a flower; Lxy: x likes y)
A. ∀x ∃y (Nx ∧ Fy ∧ Lxy)
B. ∃y ∀x (Nx → (Fy ∧ Lxy))
C. ∀x ∀y (Nx → (Fy → Lxy))
D. ∀x (Nx → ∃y (Fy ∧ Lxy))
Answer: D | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | bac1ee50-a1fc-4918-b69e-bcdaff72ad6c | Nemotron-Pretraining-Formal-Logic |
Use indirect truth tables to determine whether the following set of propositions is consistent. If the set is consistent, choose an option with a consistent valuation. (There may be other consistent valuations.)
(S ∨ O) ⊃ N
T ⊃ (N ∨ P)
O ⊃ (T ∨ S)
(N ∨ T) ⊃ P
A. Consistent. Consistent valuation when S is false, N is tr... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 66433f40-b00e-4b21-95dc-e5a2ee729d78 | Nemotron-Pretraining-Multiple-Choice |
Which of the given formulas of PL is the best symbolization of the following sentence?
Either Nina's meticulous gardening is a necessary condition for the roses to bloom, or Michelle participates in the community event if and only if Michael organizes it.
A. (G ⊃ B) ∨ (P ≡ O)
B. (B ⊃ G) ∨ (O ⊃ P)
C. (B ⊃ G) ∨ (P ≡ O)
D... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 0f58ddc3-1a7e-4816-8813-b58a8a985b39 | Nemotron-Pretraining-Multiple-Choice |
Quesion: Which of the following propositions is an immediate (one-step) consequence in Propositional Logic (PL) of the given premises?
X ⊃ (B ≡ C)
~(B ≡ C)
D ∨ X
Options:
A. X
B. ~X
C. D
D. B ≡ C
Answer: We are given the following premises in propositional logic:
1. $ X \supset (B \equiv C) $
2. $ \neg (B \equiv C) $
... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | e5710094-3c8c-4220-939c-198e1c206df7 | Nemotron-Pretraining-Formal-Logic |
Which of the given formulas of PL is the best symbolization of the following sentence?
Either Babu's successful car repair is a necessary condition for Angela to bake cornbread, or Luis waters the garden only if Angela bakes cornbread.
A. (C ⊃ R) ∨ (W ⊃ C)
B. (R ⊃ C) ∨ (C ⊃ W)
C. (R ⊃ C) ∨ (W ≡ C)
D. (C ⊃ R) ∨ ~(W ⊃ C)... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 5880b47e-cad1-4731-ae08-09864a8c1764 | Nemotron-Pretraining-Multiple-Choice |
Quesion: Select the best translation into predicate logic: Every competitive person admires Heather.
Options:
A. ∀x (C(x) → A(h, x))
B. ∀x (C(x) ∧ A(x, h))
C. ∀x (C(x) → A(x, h))
D. ∃x (C(x) → A(x, h))
Answer: To translate "Every competitive person admires Heather" into predicate logic, follow these steps:
Step 1: Ide... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 06081bbd-da81-4adf-9c8a-420ca14e0a68 | Nemotron-Pretraining-Code-Concepts |
Identify the antecedent of the following conditional proposition. Roxana will bake a special chocolate cake for her friends at her house if the Cincinnati Reds win the World Series.
A. corporate espionage is prevented at Roxana's workplace
B. Roxana will bake a special chocolate cake for her friends at her house
C. Rox... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | af0a88ef-ea86-4002-b2a0-45d865b63941 | Nemotron-Pretraining-Economics |
Quesion: Select the best translation into predicate logic. Jignesh shares some plant cuttings with his neighbors. (j: Jignesh; Px: x is a plant cutting; Nxy: x is a neighbor of y; Sxyz: x shares y with z)
Options:
A. (∃y)(∃z)(Py ∧ N j z ∧ S j y z)
B. (∃y)(∃z)(Py ∧ N z j ∧ S j z y)
C. (∃y)(∃z)(Py ∧ N z j ∧ S j y z)
D. (... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 646c18c9-f8f7-4ceb-907c-ced5c8920bc1 | Nemotron-Pretraining-Multiple-Choice |
Select the best translation into predicate logic. Some gardeners protect heirloom plants from pests. (Gx: x is a gardener; Hx: x is an heirloom plant; Px: x is a pest; Protectxyz: x protects y from z)
A. (∃x)(Gx ∧ Protectxhp)
B. (∃x)(Gx ∧ (∃y)(∃z)(Hy ∧ Pz ∧ Protectxyz))
C. (∃x)(Gx → (∃y)(∃z)(Hy ∧ Pz ∧ Protectxyz))
D. (... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 9452b0d1-2029-4101-8b31-65a78507ed45 | Nemotron-Pretraining-Formal-Logic |
Select the best English interpretation of the given argument in predicate logic.
(∀x)[R(x) ⊃ ~T(x)]
Rp
(∀x)T(x) ∨ (∃x)~O(x)
∴ (∃x)~O(x)
Where R(x): x is reserved, T(x): x loves tradition, O(x): x is orderly
A. If a person is reserved, then they do not love tradition. Pablo is reserved. Either everyone loves tradition o... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 018b1603-0a11-488d-ba16-10dad1a908a8 | Nemotron-Pretraining-Unconditional-Algorithmic |
Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
Premise 1: (Y ∧ E) ⊃ Q
Premise 2: I ⊃ O
Conclusion: Y ⊃ O
A. Valid
B. Invalid. Counterexample when Y is true, E is f... | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | c9718091-bc58-4d64-b8f4-de5b32eabbf8 | Nemotron-Pretraining-Code-Concepts |
Which of the given formulas of PL is the best symbolization of the following sentence?
Maria will debug the code only if Steven reviews the financial report.
A. M ⊃ S
B. ~S ⊃ ~M
C. M ≡ S
D. S ⊃ M
Answer: A | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | a194e900-e03d-482b-9d58-f1270892dcfb | Nemotron-Pretraining-Code-Concepts |
Select the best translation into predicate logic. Patrick serves slow-cooked barbecue to Jade. (p: Patrick; b: slow-cooked barbecue; j: Jade; Sxyz: x serves y to z)
A. Spjb
B. Spbj
C. Sbjp
D. Sjbp
Answer: B | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | 63dec026-c9fb-4ae9-8712-8953acc418c5 | Nemotron-Pretraining-Unconditional-Algorithmic |
Select the best translation into predicate logic: Every gathering that Will attends is lively.
A. (∀x)((Ax ∧ Wx) ⊃ Lx)
B. (∀x)(Ax ⊃ (Wx ∧ Lx))
C. (∀x)((Ax ∧ Lx) ⊃ Wx)
D. (∀x)(Wx ⊃ (Ax ∧ Lx))
Answer: A | cc-by-4.0 | {
"category": "Nemotron-Pretraining-Formal-Logic",
"models_used": "Qwen3-235B-A22B-Thinking-2507"
} | f81eb07a-b432-483b-ada4-90692633ebde | Nemotron-Pretraining-Economics |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 44