question stringclasses 5
values | choices sequence | answer class label 3
classes | negate_openai_prompt dict | neg_question stringclasses 5
values | fewshot_context stringclasses 1
value | ori_prompt stringclasses 5
values | neg_prompt stringclasses 5
values | fewshot_context_neg stringclasses 1
value | fewshot_context_ori stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|
Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field. | [
"0",
"1",
"2",
"3"
] | 1B | {
"content": "Given a text in the form of a short question, a question with long context, a fill in the blank query, or multiple statements. Negate the given text by making minimal changes. Only negate the main question or intent, don't negate the provided context of the question and don't complete the cloze query. R... | Are there any c in Z_3 such that Z_3[x]/(x^2 + c) is not a field? | Find all c in Z_3 such that Z_3[x]/(x^2 + c) is a field.
A. 0
B. 1
C. 2
D. 3
Answer: B | Are there any c in Z_3 such that Z_3[x]/(x^2 + c) is not a field?
A. 0
B. 1
C. 2
D. 3
Answer: D | |||
Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G. | [
"True, True",
"False, False",
"True, False",
"False, True"
] | 1B | {
"content": "Given a text in the form of a short question, a question with long context, a fill in the blank query, or multiple statements. Negate the given text by making minimal changes. Only negate the main question or intent, don't negate the provided context of the question and don't complete the cloze query. R... | Statement 1 | If aH is not an element of a factor group, then |aH| does not divide |a|. Statement 2 | If H and K are subgroups of G then HK is not a subgroup of G. | Statement 1 | If aH is an element of a factor group, then |aH| divides |a|. Statement 2 | If H and K are subgroups of G then HK is a subgroup of G.
A. True, True
B. False, False
C. True, False
D. False, True
Answer: B | Statement 1 | If aH is not an element of a factor group, then |aH| does not divide |a|. Statement 2 | If H and K are subgroups of G then HK is not a subgroup of G.
A. True, True
B. False, False
C. True, False
D. False, True
Answer: C | |||
Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements. | [
"True, True",
"False, False",
"True, False",
"False, True"
] | 2C | {
"content": "Given a text in the form of a short question, a question with long context, a fill in the blank query, or multiple statements. Negate the given text by making minimal changes. Only negate the main question or intent, don't negate the provided context of the question and don't complete the cloze query. R... | Statement 1 | Not every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 does not have 10 elements. | Statement 1 | Every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 has 10 elements.
A. True, True
B. False, False
C. True, False
D. False, True
Answer: C | Statement 1 | Not every element of a group generates a cyclic subgroup of the group. Statement 2 | The symmetric group S_10 does not have 10 elements.
A. True, True
B. False, False
C. True, False
D. False, True
Answer: A | |||
Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian. | [
"True, True",
"False, False",
"True, False",
"False, True"
] | 0A | {
"content": "Given a text in the form of a short question, a question with long context, a fill in the blank query, or multiple statements. Negate the given text by making minimal changes. Only negate the main question or intent, don't negate the provided context of the question and don't complete the cloze query. R... | Statement 1 | Is it possible for a function from a finite set onto itself to not be one to one?
Statement 2 | Is it possible for a subgroup of an abelian group to not be abelian? | Statement 1| Every function from a finite set onto itself must be one to one. Statement 2 | Every subgroup of an abelian group is abelian.
A. True, True
B. False, False
C. True, False
D. False, True
Answer: A | Statement 1 | Is it possible for a function from a finite set onto itself to not be one to one?
Statement 2 | Is it possible for a subgroup of an abelian group to not be abelian?
A. True, True
B. False, False
C. True, False
D. False, True
Answer: C | |||
Find the characteristic of the ring 2Z. | [
"0",
"3",
"12",
"30"
] | 0A | {
"content": "Given a text in the form of a short question, a question with long context, a fill in the blank query, or multiple statements. Negate the given text by making minimal changes. Only negate the main question or intent, don't negate the provided context of the question and don't complete the cloze query. R... | What is not the characteristic of the ring 2Z? | Find the characteristic of the ring 2Z.
A. 0
B. 3
C. 12
D. 30
Answer: A | What is not the characteristic of the ring 2Z?
A. 0
B. 3
C. 12
D. 30
Answer: B |
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