How do you compute the Cartesian product of two specific finite sets?

Conditions

• The sets are finite and explicitly given.

Reasoning, step by step

1. List the elements of the first set A.
2. List the elements of the second set B.
3. For each element x in A, pair it with every element y in B to form (x, y).
4. Collect all generated ordered pairs into a single set.
5. Count the total number of pairs to verify it equals |A| × |B|.

Example

Given $A = {1, 2, 3}$ and $B = {5, 6}$, pair 1 with 5 and 6 to get (1, 5) and (1, 6); pair 2 with 5 and 6 to get (2, 5) and (2, 6); pair 3 with 5 and 6 to get (3, 5) and (3, 6). The result is {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6)}.

Common misconceptions

• Missing some combinations by not pairing every element of A with every element of B.
• Writing the result as a list of numbers instead of a set of ordered pairs.
• Confusing the order of elements within the ordered pairs.

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