## Sets

# Practical Problems on Union and Intersection of Two Sets

- Let A and B be finite sets. If A ∩ B = Φ, then n (A ∪ B) = n (A) + n (B). The elements in A ∪ B are either in A or in B but not in both as A ∩ B = Φ.
- Let the Sets A − B, A ∩ B and B − A are disjoint then n (A ∪ B) = n (A − B) + n (A ∩ B) + n (B − A) ⇒ n (A ∪ B) = n (A) + n (B) - n (A ∩ B)

### View the Topic in this video From 25:50 To 42:43

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1. a) n (A ∪ B) = n (A) + (B) − n (A ∩ B)

b) n (A ∪ B) = n (A) + n (B), if A and B are disjoint.

c) n (A − B) = n (A) − n (A ∩ B)

d) n (A Δ B) = n (A) + n (B) − 2n (A ∩ B)

2. n (A ∪ B ∪ C) = n (A) + n (B) + n (C) − n (A ∩ B) − n (B ∩ C) − n (A ∩ C) + n (A ∩ B ∩ C)

3. a) n (A' ∪ B') = n (A ∩ B)' = n (U) − n (A ∩ B)

b) n (A' ∩ B') = n (A ∪ B)' = n (U) − n (A ∪ B)

c) n (B − A) = n (B) − n (A ∩ B)

d) n(A ∩ B) = n(A ∪ B) – n(A ∩ B') – n(A' ∩ B)