Cartesian product A × B for small finite sets: Let A = {1, 2} and B = {2, 3}. Evaluate A × B.

Introduction / Context:
The Cartesian product A × B is the set of all ordered pairs (a, b) with a ∈ A and b ∈ B. For small finite sets, listing pairs systematically by fixing the first component is best practice.

Given Data / Assumptions:

• A = {1, 2}
• B = {2, 3}

Concept / Approach:
Form pairs by taking each element of A and pairing it with each element of B in order. Preserve the order (a first, then b) as order matters in ordered pairs.

Step-by-Step Solution:
For a = 1: (1,2), (1,3)For a = 2: (2,2), (2,3)Hence A × B = {(1,2), (1,3), (2,2), (2,3)}

Verification / Alternative check:
Count check: |A| * |B| = 2 * 2 = 4 pairs; four listed—complete.

Why Other Options Are Wrong:
(a) reverses the order and omits pairs; (b) misses (2,2); “None of these” is unnecessary since (c) is exact.

Common Pitfalls:
Confusing A × B with B × A or forgetting that order matters, leading to missing pairs.

Final Answer:
{(1, 2), (1, 3), (2, 2), (2, 3)}