ITPEC FE Morning October 2021 Question 3
ITPEC FE Morning October 2021 — Question 3 of 80
Distributive Law of Sets — identify which set equality holds for three sets.
The distributive law states:
- (A ∩ C) ∪ (B ∩ C) = (A ∪ B) ∩ C
- (A ∪ C) ∩ (B ∪ C) = (A ∩ B) ∪ C
Think of ∩ as multiplication and ∪ as addition: AC + BC = (A+B)C.
Why not others (counterexample A={1,2}, B={2,3}, C={1,3}):
- (a) (A ∪ B) ∩ (A ∩ C) = {1} but B ∩ (A ∪ C) = {2,3} — not equal
- (b) (A ∪ B) ∩ C = {1,3} but (A ∪ C) ∩ (B ∪ C) = {1,2,3} — not equal
- (c) (A ∩ C) ∪ (B ∩ A) = {1,2} but (A ∩ B) ∪ (B ∩ C) = {2,3} — not equal
Key rule: Distributive law works exactly like algebra: ∩ distributes over ∪ and vice versa.
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