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Question
If A = {b, c, e, g, h}, B = {a, c, d, g, i}, and C = {a, d, e, g, h}, then show that A – (B ∩ C) = (A – B) ∪ (A – C)
Solution
A = {b, c, e, g, h}
B = {a, c, d, g, i}
C = {a, d, e, g, h}
B ∩ C = {a, c, d, g, i} ∩ {a, d, e, g, h}
= {a, d, g}
A – (B ∩ C) = {b, c, e, g, h} – {a, d, g}
= {b, c, e, h} ...(1)
A – B = {b, c, e, g, h} – {a, c, d, g, i}
= {b, e, h}
A – C = {b, c, e, g, h} – {a, d, e, g, h}
= {b, c}
(A – B) ∪ (A – C) = {b, e, h} ∪ {b, c}
= {b, c, e, h) ...(2)
From (1) and (2) we get
A – (B ∩ C) = (A – B) ∪ (A – C)
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