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TISSNET Cartesian Product Relations — practice questions

Explore 16 free Cartesian Product Relations questions in TISSNET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Cartesian Product Relations questions and exercises with answers

Showing questions 1–16 of 16.

Given P = {a, b} and Q = {1, 2}, the cartesian product P × Q isRead the answer and worked solution →If n(A) = 3 and n(B) = 4, then n(A × B) =Read the answer and worked solution →Two ordered pairs (x, y) and (a, b) are equal if and only ifRead the answer and worked solution →If (x + 1, y − 2) = (3, 1), then x and y equalRead the answer and worked solution →R × R, where R is the set of real numbers, representsRead the answer and worked solution →Let A = {1, 2, 3}, B = {3, 4}, C = {4, 5, 6}. The set A × (B ∩ C) isRead the answer and worked solution →If A × B = {(p, q), (p, r), (m, q), (m, r)}, then A and B areRead the answer and worked solution →Let P = {1, 2}. Then P × P × P contains how many ordered triples?Read the answer and worked solution →Which statement is TRUE for any non-empty sets P and Q?Read the answer and worked solution →If A or B is the empty set, then A × B equalsRead the answer and worked solution →Given P = {a, b, c} and Q = {r}, the cartesian product Q × P isRead the answer and worked solution →If A × B has 6 elements and three of these are (1, 2), (2, 3), (3, 3), then A and B areRead the answer and worked solution →Which identity is ALWAYS TRUE for arbitrary sets A, B, C?Read the answer and worked solution →If P = {m, n} and Q = {n, m}, then P × Q equalsRead the answer and worked solution →Let A = {1, 2}, B = {3, 4}. Then A × (B ∩ ∅) isRead the answer and worked solution →If n(A × B) = pq and (A × B) ∩ (A × C) = A × (B ∩ C), then for which choice is the intersection MAXIMISED?Read the answer and worked solution →

Worked practice questions

Given P = {a, b} and Q = {1, 2}, the cartesian product P × Q is

  1. {(1, a), (1, b), (2, a), (2, b)}
  2. {a, b, 1, 2}
  3. {(a, b), (1, 2)}
  4. {(a, 1), (b, 1), (a, 2), (b, 2)}
Show answer and solution

Correct answer: D. {(a, 1), (b, 1), (a, 2), (b, 2)}

P × Q is the set of ordered pairs (p, q) with p ∈ P and q ∈ Q. Order matters P × Q ≠ Q × P in general.

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If n(A) = 3 and n(B) = 4, then n(A × B) =

  1. 7
  2. 12
  3. 16
  4. 9
Show answer and solution

Correct answer: B. 12

|A × B| = |A| × |B| = 3 × 4 = 12.

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Two ordered pairs (x, y) and (a, b) are equal if and only if

  1. x + y = a + b
  2. x · y = a · b
  3. x = b and y = a
  4. x = a and y = b
Show answer and solution

Correct answer: D. x = a and y = b

Equality of ordered pairs requires corresponding components to be equal in order. Swapping the components changes the pair.

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