Video: Identifying the Sets That Multiply to Make a Given Cartesian Product

Kathryn Kingham

Which of the following Cartesian products would give the result {(20, 37), (20, 11)}? [A] {20} × {37} [B] {20} × {11} [C] {20} × {37, 11} [D] {37, 11} × {20}

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Video Transcript

Which of the following Cartesian products would give the result the set 20, 37 and 20, 11?

Let’s think about what we know about Cartesian products. Cartesian products is the set A times the set B. This multiplication of the two sets creates ordered pairs, where the first element is from set A and the second element is from set B.

We’ve been given the product, and we need to find the two sets that were multiplied together. We know that the first element in the ordered pair must come from set A. And that means that the first set here must be the set that includes 20. And that means we can eliminate option d.

We know that the second element from the ordered pair comes from set B. And for us, that means that we have both 37 and 11 in set B. Set 20 multiplied by set 37, 11 would give the result of the order pairs 20, 37 and 20, 11.

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