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If A = {a, b, c, d, e}, B = {a, c, e, g}, and C = {b, e, f, g} verify that: (i) A ∩ (B – C) = (A ∩ B) – (A ∩ C) (ii) A – (B ∩ C) = (A – B) ∪ (A – C) |
Answer» (i) B - C represents all elements in B that are not in C B - C = {a, c} A∩(B - C) = {a, c} A∩B = {a, c, e} A∩C = {b, e} (A∩B) - (A∩C) = {a, c} A∩(B - C) = (A∩B) - (A∩C) Hence proved (ii) B∩C = {e, g} A - (B∩C) = {a, b, c, d} (A - B) = {b, d} (A - C) = {a, c, d} (A - B)∪(A - C) = {a, b, c, d} A - (B∩C) = (A - B)∪(A - C) Hence proved |
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