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Question
If A = {– 2, 0, 1, 3, 5}, B = {–1, 0, 2, 5, 6} and C = {–1, 2, 5, 6, 7}, then show that A – (B ∪ C) = (A – B) ∩ (A – C)
Solution
A = {−2, 0, 1, 3, 5}
B = {−1, 0, 2, 5, 6}
C = {−1, 2, 5, 6, 7}
B ∪ C = {−1, 0, 2, 5, 6} ∪ {−1, 2, 5, 6, 7}
= {−1, 0, 2, 5, 6, 7}
A – (B ∪ C) = {−2, 0, 1, 3, 5} – {−1, 0, 2, 5, 6, 7}
= {−2, 1, 3} ...(1)
A – B = {−2, 0, 1, 3, 5} – {−1, 0, 2, 5, 6}
= {−2, 1, 3}
A – C = {−2, 0, 1, 3, 5} − {−1, 2, 5, 6, 7}
= {−2, 0, 1, 3}
(A − B) ∩ (A − C) = {−2, 1, 3} ∩ {−2, 0, 1, 3}
= {−2, 1, 3} ...(2)
From (1) and (2) we get
A – (B ∪ C) = (A – B) ∩ (A – C).
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