Question

17. Is the operation of forming Cartesian products commutative? Explain why or why not.

Choose the correct answer below.
OA. The operation of forming Cartesian products is commutative because order does not matter in
the definition of a Cartesian product.
OB. The operation of forming Cartesian products is not commutative because part of the definition of
a Cartesian product is the order of the elements generated by the two sets.
OC.
The operation of forming Cartesian products is commutative because a Cartesian product is
multiplication and multiplication is commutative.
O D. The operation of forming Cartesian products is not commutative because multiplication is not
commutative.

Answer 1

Answer: Choice B

The operation of forming Cartesian products is not commutative because part of the definition of a Cartesian product is the order of the elements generated by the two sets.

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Step-by-step explanation:

Let's go over an example. We'll have these two sets

A = {1,2}

B = {3,4}

The cartesian product is this set of ordered pairs

A x B= {(1,3), (1,4), (2,3), (2,4)}

Each (x,y) pair has x as a value from the first set mentioned (A), and y a value from the second set mentioned (B). It might help to make a 2 by 2 table.

If we swap the order of set A and B then we have

B x A = {(3,1), (4,1), (3,2), (4,2)}

We can see that A x B does not equal B x A in this case. Therefore, the cartesian product operation is not commutative. The order matters.

Side note: Two sets are equal when they are subsets of each other.