SET007 · Sets, relations & logic · Classes 9–11
Union of sets
The union A ∪ B contains every element that is in A or in B (or both). Common elements are listed once.
A ∪ BUnion of sets
📐 Formula
n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
✏️ Worked example
U = {1…12}: multiples of 2 (6 elements) ∪ multiples of 3 (4 elements) = {2, 3, 4, 6, 8, 9, 10, 12}, 6 + 4 − 2 = 8 elements.
🌍 Where it is used
Combining lists: students who play cricket or football.
❓ Quick check
{1, 2} ∪ {2, 3} = ?
🏋️ Practice
Easy{a, b} ∪ {c} = ?
Answer: {a, b, c}
Mediumn(A) = 10, n(B) = 8, n(A ∩ B) = 3. n(A ∪ B)?
Answer: 15
ChallengeA ∪ ∅ = ?
Answer: A