instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Calculate the remainder when 1184 is divided by 125.\n | 59\n | ibivibiv/math_instruct | |
What is the next term in -3167, -3302, -3657, -4340, -5459, -7122?\n | -9437\n | ibivibiv/math_instruct | |
Four letters picked without replacement from qtqtbqbqttqbbqqb. What is prob of picking 2 t and 2 b?\n | 3/91\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-14.5009 - 62.3624) - 66.3878 | -143.2511 | ibivibiv/math_instruct | |
Calculate prob of sequence taff when four letters picked without replacement from {f: 7, d: 1, t: 5, a: 5}.\n | 35/2448\n | ibivibiv/math_instruct | |
Round -0.00012311283 to five dps.\n | -0.00012\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {f: 1, h: 1, k: 2}. What is prob of sequence kkh?\n | 1/12\n | ibivibiv/math_instruct | |
Three letters picked without replacement from {n: 3, x: 3}. Give prob of sequence xxn.\n | 3/20\n | ibivibiv/math_instruct | |
-0.5*0.1045\n | -0.05225\n | ibivibiv/math_instruct | |
What is 859902.8 decades in millennia?\n | 8599.028\n | ibivibiv/math_instruct | |
Simplify (((g*g**(1/6))**(-23))**4)**(-2/105) assuming g is positive.\n | g**(92/45)\n | ibivibiv/math_instruct | |
Let h = 6 + -4. Let p(x) = -14*x + 21. Let m(i) = 7*i - 11. Let c(w) = -11*m(w) - 6*p(w). Let y be c(h). What is the greatest common divisor of y and 1?\n | 1\n | ibivibiv/math_instruct | |
Let m(n) be the third derivative of -n**6/4 + 29*n**5/60 - 47*n**2. Find the third derivative of m(t) wrt t.\n | -180\n | ibivibiv/math_instruct | |
What is (-35)/70*2/3?\n | -1/3\n | ibivibiv/math_instruct | |
What is next in 1950, 1953, 1956, 1959, 1962?\n | 1965\n | ibivibiv/math_instruct | |
Simplify (z**(-4)*z/z**0)/((z**(-3)/z)/(z**6/z)) assuming z is positive.\n | z**6\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 7044 and 96?\n | 12\n | ibivibiv/math_instruct | |
Let j(a) = 34*a - 1. Calculate j(1).\n | 33\n | ibivibiv/math_instruct | |
What is the biggest value in 0.22, -1, -0.02, 3/2, -1/171, -3?\n | 3/2\n | ibivibiv/math_instruct | |
Round 0.000015607151 to 6 decimal places.\n | 0.000016\n | ibivibiv/math_instruct | |
Let h be (0 - 0) + -10 + 9. Which is the second biggest value? (a) h (b) -11 (c) 0.5\n | a\n | ibivibiv/math_instruct | |
Let m(k) = k**3 + 5*k**2 + 5*k - 1. Let q be m(-4). Let z = -232 - -231.249. Let f = z + 0.251. Which is the closest to f? (a) -2 (b) q (c) -3\n | a\n | ibivibiv/math_instruct | |
Let x be 4*(1/(-5))/((-4)/10). Solve -c - 17 = 5*b - x*c, 3*b + 3*c = -3 for b.\n | -3\n | ibivibiv/math_instruct | |
Simplify (-2*(-1 + sqrt(605))*2 - ((4 + 1*sqrt(605) - sqrt(605)) + (sqrt(605) - ((sqrt(605) - (sqrt(605) + -1)) + 5))))**2.\n | -660*sqrt(5) + 15161\n | ibivibiv/math_instruct | |
Let a(j) = -13*j**3 - 2*j**2 - 5*j - 9. What is the remainder when a(-2) is divided by 20?\n | 17\n | ibivibiv/math_instruct | |
Let y = -14 + 15. Sort 2, 11, y in ascending order.\n | y, 2, 11\n | ibivibiv/math_instruct | |
Is 18887709 a prime number?\n | False\n | ibivibiv/math_instruct | |
What is 12613864 to the power of 1/3, to the nearest integer?\n | 233\n | ibivibiv/math_instruct | |
Work out 7 + -423.\n | -416\n | ibivibiv/math_instruct | |
Express -24 + 4*j + 2*j - 76 - 8*j as n*j + w and give w.\n | -100\n | ibivibiv/math_instruct | |
Solve -76 = 17*w - 59 for w.\n | -1\n | ibivibiv/math_instruct | |
Which is the third biggest value? (a) 15/11722 (b) -0.3 (c) -34.03\n | c\n | ibivibiv/math_instruct | |
Evaluate (-34)/(((-76)/10830*-57)/((-2)/50)).\n | 17/5\n | ibivibiv/math_instruct | |
What is the third root of 2693 to the nearest integer?\n | 14\n | ibivibiv/math_instruct | |
Round -0.0362558758 to five decimal places.\n | -0.03626\n | ibivibiv/math_instruct | |
Let h(k) = -18*k**2 + 27*k - 10. Let b(m) = 6*m**2 + 2. Let s(n) = -2*b(n) - h(n). What is s(5)?\n | 21\n | ibivibiv/math_instruct | |
Let w(a) = -a**2 + 2*a. Let n = -41 - -39. What is w(n)?\n | -8\n | ibivibiv/math_instruct | |
Find c, given that c**5 - 151*c**4/2 + 2907*c**3/2 - 11012*c**2 + 31264*c - 13056 = 0.\n | 1/2, 8, 51\n | ibivibiv/math_instruct | |
Let a(j) = 0*j - 21 + 6 - 15*j - 3*j**2. Let m(s) = s**2 + 4*s + 4. Determine 4*a(q) + 15*m(q).\n | 3*q**2\n | ibivibiv/math_instruct | |
Which is the closest to 2/5? (a) 6 (b) -294 (c) -38 (d) -0.04 (e) -1\n | d\n | ibivibiv/math_instruct | |
Let o = 50 - 43. Let v(h) = 0*h**2 - o*h + 3*h**2 + 8 + 6*h - 18*h. Does 14 divide v(8)?\n | False\n | ibivibiv/math_instruct | |
Let i = -4775/16 + 296. Let j = -5121429461 + 39762778280201/7764. Let d = j - -2/1941. What is the common denominator of i and d?\n | 48\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Domain of discourse and quantifying in predicate logic
I am struggling with an idea about how quantifiers relate to domains of discourse. Given a statement "$x$ is divisible by $2$" represented by the predicate $D(x)$,the ... | The issue you are grappling with revolves around the concept of a domain of discourse and its relationship with quantifiers in predicate logic. To understand this better, let us first examine these two fundamental ideas separately before delving into their interplay.
A domain of discourse, also known as the universe ... | ibivibiv/math_instruct | |
Let b(m) = -3*m**3 + m**2 + 5*m + 4. Suppose -3*h = h + 8. What are the prime factors of b(h)?\n | 2, 11\n | ibivibiv/math_instruct | |
Let y(x) be the first derivative of -2 + 4 + 2*x**2 + 0 - x. Is y(5) a composite number?\n | False\n | ibivibiv/math_instruct | |
Expand (0*u + 0*u - u)*(3806*u - 1260*u - 1271*u - 1269*u + 597).\n | -6*u**2 - 597*u\n | ibivibiv/math_instruct | |
Let p be (-1)/(52/(-252)) + -5. What is the nearest to -1 in -2, p, -0.4?\n | -0.4\n | ibivibiv/math_instruct | |
Let u = 2 - 2. Suppose -3*s = 2*q - 203, 5*s + u*s = -2*q + 333. Is s a prime number?\n | False\n | ibivibiv/math_instruct | |
What is the product of 1.08 and 490636.2?\n | 529887.096\n | ibivibiv/math_instruct | |
Calculate 0.05 + -2784064037192.\n | -2784064037191.95\n | ibivibiv/math_instruct | |
Sort -80, -3, 3, 5.\n | -80, -3, 3, 5\n | ibivibiv/math_instruct | |
Suppose 2 - 17 = -3*z. Suppose -2*a + 33 = -z. Suppose 19*f - 35 = 18*f. Calculate the remainder when f is divided by a.\n | 16\n | ibivibiv/math_instruct | |
Convert 2 (base 10) to base 2.\n | 10\n | ibivibiv/math_instruct | |
Express -4 + 0 + 4 + 6*y in the form t*y + d and give t.\n | 6\n | ibivibiv/math_instruct | |
Let d be 25*(2 + (-3 + 6)*-1). Let s(f) = f**3 + 11*f**2 - 11*f - 13. Suppose -l + 20 = -2*y, -3*l = 2*l + 20. Let j be s(y). Is j at least as big as d?\n | True\n | ibivibiv/math_instruct | |
Let y = 19 + -19. Solve -u + y*k + 4*k + 24 = 0, u - 29 = 5*k for u.\n | 4\n | ibivibiv/math_instruct | |
What is 1*11/22*6?\n | 3\n | ibivibiv/math_instruct | |
Let d be -8 - -14 - (-1 + 4). Suppose 5*c = d*c + 8. Suppose v - n = -2105, 12 - 32 = -c*n. Round v to the nearest 1000.\n | -2000\n | ibivibiv/math_instruct | |
Let m(r) = r**3 + 12*r**2 - r - 24. Let a be m(-12). Let t be ((-3)/a - 0)*52. Let o(d) = d**2 - 14*d + 5. Let v be o(t). Which is bigger: v or 0.6?\n | 0.6\n | ibivibiv/math_instruct | |
Round -0.07787321 to four decimal places.\n | -0.0779\n | ibivibiv/math_instruct | |
Let p(s) be the second derivative of s**3/3 + 11*s**2/2 - 3*s. Let x be p(-8). Let g be (-1)/(x/((-15)/(-9))). Which is smaller: g or 1?\n | g\n | ibivibiv/math_instruct | |
What is prob of picking 1 i and 3 g when four letters picked without replacement from {g: 8, i: 3, a: 2, c: 4}?\n | 6/85\n | ibivibiv/math_instruct | |
What is prob of sequence amva when four letters picked without replacement from ciaviaiqivmcqi?\n | 1/6006\n | ibivibiv/math_instruct | |
Let b = 3.0721 + -0.0721. Let k = 6.4 + -6. Let g = -0.45 + k. Put b, g, -3/8 in increasing order.\n | -3/8, g, b\n | ibivibiv/math_instruct | |
What is 538 minutes after 7:50 PM?\n | 4:48 AM\n | ibivibiv/math_instruct | |
b"What is the pth term of 3134, 3120, 3068, 2960, 2778, 2504, 2120, 1608?\n" | -3*p**3 - p**2 + 10*p + 3128\n | ibivibiv/math_instruct | |
Expand -4*b + 4*b - 2*b**4 + (12*b + 2 - 2)*(3*b**3 + 2*b**3 - b**3).\n | 46*b**4\n | ibivibiv/math_instruct | |
Let s(g) be the second derivative of 2*g**3/3 - g**2/2 + 5*g. Let v(o) = -17*o + 5. Give -9*s(h) - 2*v(h).\n | -2*h - 1\n | ibivibiv/math_instruct | |
Suppose -17 - 423 = 4*w. Let n = w + 112. Suppose -4*d + 330 = n*y, 2*d + 633 = 4*y + 13. Is y composite?\n | False\n | ibivibiv/math_instruct | |
Let t(w) = -4*w**2 + w - 9. Let k(g) = -2*g**2 - 4. What is 5*k(s) - 2*t(s)?\n | -2*s**2 - 2*s - 2\n | ibivibiv/math_instruct | |
Let i(v) = v**2 - 8*v - 3. Let a(f) = 3 + 3*f - 2*f + 6*f - f**2. Let o(q) = 5*a(q) + 4*i(q). Determine o(3).\n | 3\n | ibivibiv/math_instruct | |
Sort 4, -92, -4, 9 in ascending order.\n | -92, -4, 4, 9\n | ibivibiv/math_instruct | |
Suppose -7*g + 3*g + 3*i - 5 = 0, 11 = 5*g + 2*i. Put g, 0, 2 in decreasing order.\n | 2, g, 0\n | ibivibiv/math_instruct | |
Find the second derivative of -3 - 72*n + 25*n + 21*n + 24*n + 1 + 196*n**2 wrt n.\n | 392\n | ibivibiv/math_instruct | |
(-208)/(-42)*(-30)/(-40) - 4\n | -2/7\n | ibivibiv/math_instruct | |
What is 16853908 to the power of 1/2, to the nearest integer?\n | 4105\n | ibivibiv/math_instruct | |
Which is smaller: 872/129 or 7?\n | 872/129\n | ibivibiv/math_instruct | |
What is 0.0808750144 rounded to six decimal places?\n | 0.080875\n | ibivibiv/math_instruct | |
What is -2 + (5 - 0) - -2?\n | 5\n | ibivibiv/math_instruct | |
What is the first derivative of -11 + 226*k**3 - 7 - 239*k**3 wrt k?\n | -39*k**2\n | ibivibiv/math_instruct | |
Suppose -k = 5*t - 19, 9 = 6*t - 3*t. Let x = -1214 + 1246. Calculate the greatest common factor of x and k.\n | 4\n | ibivibiv/math_instruct | |
Simplify ((o/(o/o**(-8)))/(o/(o*o**(-10))))**9 assuming o is positive.\n | o**(-162)\n | ibivibiv/math_instruct | |
Solve 4*q - 4*f = 21 + 31, 6*q + 65 = -5*f for q.\n | 0\n | ibivibiv/math_instruct | |
Simplify ((u*u**(-6))/u**3)/((u/(u/(u*u/((u*(u*u**3)/u)/u)*u*u))*u)/u)**(-2) assuming u is positive.\n | u**(-6)\n | ibivibiv/math_instruct | |
Let i be (-1)/2*-3*(-20)/(-5). Let u be (20/i)/5*3. Suppose -n - 3*n = 0. Solve -u*x = -n*x for x.\n | 0\n | ibivibiv/math_instruct | |
Solve -v + 3*n + 4 = v, 5*v + 4*n + 36 = 0 for v.\n | -4\n | ibivibiv/math_instruct | |
How many seconds are there in 7/15 of a minute?\n | 28\n | ibivibiv/math_instruct | |
Let z = 100 + -91.8. Let m = z - 9.2. Let t be (9/6 + -1)/(-18). Which is smaller: t or m?\n | m\n | ibivibiv/math_instruct | |
Solve -11*a + 7*a = 0 for a.\n | 0\n | ibivibiv/math_instruct | |
-67 * -0.1192\n | 7.9864\n | ibivibiv/math_instruct | |
Let v be (1 + -4)*-1 - (1 + 1). Let x be v - ((-741984)/14 + 4/(-28)). Round x to the nearest 10000.\n | 50000\n | ibivibiv/math_instruct | |
Which is the closest to 1/2? (a) -3 (b) 495 (c) 5/3 (d) 0 (e) -16\n | d\n | ibivibiv/math_instruct | |
What is next in 202, 982, 1760, 2536, 3310?\n | 4082\n | ibivibiv/math_instruct | |
What is the biggest value in 1/16, 76, 0.73?\n | 76\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {u: 3, o: 5, d: 2, c: 3, z: 2}. What is prob of sequence oc?\n | 1/14\n | ibivibiv/math_instruct | |
Let b = -178 - -182. Find the common denominator of (1 + 578/b)/((-300)/25) and 145/12.\n | 24\n | ibivibiv/math_instruct | |
Suppose -5*d + 118 = -62. Suppose -2*o - 3 = j + 170, -3*o = -4*j - 736. Let a = 199 + j. Calculate the highest common factor of d and a.\n | 18\n | ibivibiv/math_instruct | |
What is -998343.31 rounded to the nearest 1000?\n | -998000\n | ibivibiv/math_instruct | |
Solve 0 = -81*c + 89*c - 56 for c.\n | 7\n | ibivibiv/math_instruct | |
Calculate (2 - -1) + -29 + 32.\n | 6\n | ibivibiv/math_instruct |
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