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 how many in B × A respectively?
Both A × B and B × A contain 6 ordered pairs, because the count of pairs in a Cartesian product is the product of the sizes of the two sets, 3 × 2 = 6, and multiplication is commutative even though the pairs differ.
- A6 and 6Correct
- B5 and 5
- C6 and 3
- D9 and 4
Explanation
n(A)=3 and n(B)=2. The number of ordered pairs in A × B is 3 × 2 = 6. B × A also has 2 × 3 = 6 pairs, though the pairs themselves differ. Option 5 and 5 wrongly adds the sizes.
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