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GRE Unit 1A1: Relations, Functions and Graphs — practice questions — page 3

Explore 73 free Unit 1A1: Relations, Functions and Graphs questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Unit 1A1: Relations, Functions and Graphs questions and exercises with answers

Showing questions 61–73 of 73.

If two ordered pairs (a, b) and (c, d) are equal, then:Read the answer and worked solution →If n(A) = p and n(B) = q, then n(A × B) equals:Read the answer and worked solution →A relation R from set A to set B is, by definition:Read the answer and worked solution →If (x + 1, y - 2) = (3, 1), find x and y.Read the answer and worked solution →Let A = {1, 2, 3} and B = {3, 4}. Find n(A × B):Read the answer and worked solution →Let A = {1, 2} and B = {3, 4}. The total number of relations from A to B is:Read the answer and worked solution →If A × B = {(p, q), (p, r), (m, q), (m, r)}, then A and B are:Read the answer and worked solution →The Cartesian product A × A has 9 elements, two of which are (-1, 0) and (0, 1). The set A is:Read the answer and worked solution →A relation R is defined on A = {1, 2, 3, 4, 6} by R = {(a, b): b is exactly divisible by a; a, b ∈ A}. The domain of R is:Read the answer and worked solution →Identify the function h(x) = x^(2/3) + 2x. Which of the following is INCORRECT?Read the answer and worked solution →Let A = {1, 2} and B = {3, 4}. The number of subsets of A × B is:Read the answer and worked solution →R = {(x, x^3) : x is a prime number less than 10} in roster form is:Read the answer and worked solution →Let A = {x, y, z} and B = {1, 2}. The number of relations from A to B is:Read the answer and worked solution →

Worked practice questions

If two ordered pairs (a, b) and (c, d) are equal, then:

  1. a + b = c + d
  2. a = d and b = c
  3. a = c and b = d
  4. a × b = c × d
Show answer and solution

Correct answer: C. a = c and b = d

Equality of ordered pairs requires the FIRST elements equal AND the SECOND elements equal. **So (a, b) = (c, d) iff a = c and b = d.**

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If n(A) = p and n(B) = q, then n(A × B) equals:

  1. p + q
  2. |p - q|
  3. p^q
  4. p × q
Show answer and solution

Correct answer: D. p × q

The Cartesian product A × B has pq ordered pairs — for each of the p elements of A you can pair with each of the q elements of B.

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A relation R from set A to set B is, by definition:

  1. An element of A
  2. A subset of A × B
  3. The set A × B itself
  4. A subset of B × A only
Show answer and solution

Correct answer: B. A subset of A × B

A relation from A to B is any subset of A × B. We isolate it by describing a connection between the first and second elements of the ordered pairs.

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More Mathematics topics

MathematicsStatistics and ProbabilityArithmetic ProgressionSets and RelationsQuadratic EquationsReal Numbers and PolynomialsUnit 6B: Definite Integration & Riemann SumsUnit 1B1: Limit Concepts and Graphical Limits