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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram

Set A = {2, 4, 6} and set B = {1, 3}. How many ordered pairs are there in the Cartesian product A × B, and is B × A equal to A × B?

A × B has 3 × 2 = 6 ordered pairs. B × A also has 6 pairs, but the pairs are reversed, such as (1,2) instead of (2,1), so the two products are not equal. Cartesian product is not commutative unless the two sets are identical.

  1. A6 ordered pairs; B × A equals A × B
  2. B5 ordered pairs; B × A equals A × B
  3. C5 ordered pairs; B × A does not equal A × B
  4. D6 ordered pairs; B × A does not equal A × BCorrect

Explanation

n(A × B) = n(A) × n(B) = 3 × 2 = 6. A × B has pairs like (2,1) while B × A has pairs like (1,2). Since ordered pairs differ, the two products are different sets. The 'equal' option is wrong because the Cartesian product is not commutative unless A = B.

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