What is the Cartesian product of two sets A and B?

Conditions

• A and B are arbitrary sets.

Reasoning, step by step

1. Identify the two sets A and B.
2. Form ordered pairs (x, y) by selecting an element x from A and an element y from B.
3. Collect all such possible ordered pairs into a new set.
4. Express the result using set-builder notation: $A \times B$ = {(x, y) | $x \in A$, $y \in B$}.

Example

If $A = {1, 2, 3}$ and $B = {5, 6}$, then $A \times B = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6)}$.

Common misconceptions

• Believing that the Cartesian product is a set of unordered pairs.
• Thinking that the elements of A and B must be numbers.
• Assuming that $A \times B$ is the same as $B \times A$.

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