SET013 · Sets, relations & logic · Classes 11–12
Cartesian product
The Cartesian product A × B is the set of all ordered pairs (a, b) with a ∈ A and b ∈ B.
A × BCartesian product
📐 Formula
A × B = {(a, b) : a ∈ A, b ∈ B}; n(A × B) = n(A) × n(B)
✏️ Worked example
A = {1, 2, 3}, B = {a, b}: A × B has 3 × 2 = 6 pairs, (1, a), (1, b), (2, a), …
🌍 Where it is used
All outfits from shirts × trousers; coordinates ℝ × ℝ.
❓ Quick check
n(A) = 4, n(B) = 5. n(A × B) = ?
🏋️ Practice
Easy{1} × {x, y} = ?
Answer: {(1, x), (1, y)}
MediumIs (2, 1) the same pair as (1, 2)?
Answer: No: order matters
ChallengeIf A × B has 12 pairs and n(A) = 3, n(B) = ?
Answer: 4