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GRE Sets and Relations — practice questions

Explore 101 free Sets and Relations questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Sets and Relations questions and exercises with answers

Showing questions 1–30 of 101.

Which of the following is a linear equation in one variable?Read the answer and worked solution →Solve for x: 3x = 2x + 18Read the answer and worked solution →Solve for t: 5t − 3 = 3t − 5Read the answer and worked solution →Solve for x: 5x + 9 = 5 + 3xRead the answer and worked solution →If 4z + 3 = 6 + 2z, what is the value of z?Read the answer and worked solution →Solve for x: 8x + 4 = 3(x − 1) + 7Read the answer and worked solution →Solve for x: x = (4/5)(x + 10)Read the answer and worked solution →Solve for x: (2x/3) + 1 = (7x/15) + 3Read the answer and worked solution →Solve for y: 2y + 5/3 = 26/3 − yRead the answer and worked solution →Solve for x: (x − 5)/3 = (x − 3)/5Read the answer and worked solution →Inverse of function f exists if and only if f is:Read the answer and worked solution →Composition of functions (g ∘ f)(x) =Read the answer and worked solution →If A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6, 7}, find A ∩ B:Read the answer and worked solution →Number of subsets of {1, 2, 3, 4, 5} with exactly 3 elements:Read the answer and worked solution →For 3 sets A, B, C: n(A ∪ B ∪ C) =Read the answer and worked solution →100 students; 50 like math, 60 like physics, 30 like both. Find students who like neither:Read the answer and worked solution →Number of one-one functions from {1, 2, 3} to {a, b, c, d, e}:Read the answer and worked solution →Equivalence relation requires:Read the answer and worked solution →For sets A, B: A × B = B × A iff:Read the answer and worked solution →Range of f(x) = sin(x) from R to R:Read the answer and worked solution →|A| = 5, |B| = 3. Number of relations from A to B:Read the answer and worked solution →For f: A → B and g: B → C, (g ∘ f)⁻¹ =Read the answer and worked solution →Function f(x) = (x-1)/(x+2) on R - {-2}. f is bijection from R - {-2} to R - {?}:Read the answer and worked solution →Equivalence classes of 'congruent mod 3' on Z:Read the answer and worked solution →Number of one-one and onto (bijective) functions from {1,2,3} to {1,2,3}:Read the answer and worked solution →For function f(x) = ax + b (a ≠ 0), inverse is:Read the answer and worked solution →For f: R → R, f(x) = x³, f is:Read the answer and worked solution →Distributive law: A ∩ (B ∪ C) =Read the answer and worked solution →Inverse image f⁻¹(B) under f: X → Y for B ⊆ Y:Read the answer and worked solution →Number of equivalence relations on set {a, b, c}:Read the answer and worked solution →

Worked practice questions

Which of the following is a linear equation in one variable?

  1. x² + 1 = 0
  2. 2x + y = 5
  3. 5x − 3 = 7
  4. xy = 10
Show answer and solution

Correct answer: C. 5x − 3 = 7

A linear equation in one variable has exactly one variable and the highest power of that variable is 1. Only 5x − 3 = 7 satisfies both conditions.

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Solve for x: 3x = 2x + 18

  1. x = 6
  2. x = 9
  3. x = 18
  4. x = 36
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Correct answer: C. x = 18

Subtract 2x from both sides: 3x − 2x = 18, so x = 18.

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Solve for t: 5t − 3 = 3t − 5

  1. t = −1
  2. t = 1
  3. t = −4
  4. t = 4
Show answer and solution

Correct answer: A. t = −1

Transpose 3t to the left and −3 to the right: 5t − 3t = −5 + 3, so 2t = −2 and t = −1.

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More Mathematics topics

MathematicsStatistics and ProbabilityArithmetic ProgressionQuadratic EquationsReal Numbers and PolynomialsUnit 1A1: Relations, Functions and GraphsUnit 6B: Definite Integration & Riemann SumsUnit 1B1: Limit Concepts and Graphical Limits