

InterviewSolution
1. |
For all sets A, B and C, show that (A – B) ∩ (A – C) = A – (B ∪ C) |
Answer» According to the question, There are three sets A, B and C To show: (A – B) ∩ (A – C) = A – (B ∪ C) Let x ∈ (A – B) ∩ (A – C) ⇒ x ∈ (A – B) and x ∈ (A – C) ⇒ (x ∈ A and x ∉ B) and (x ∈ A and x ∉ C) ⇒ x ∈ A and (x ∉ B and x ∉ C) ⇒ x ∈ A and x ∉ (B ∪ C) ⇒ x ∈ A – (B ∪ C) ⇒ (A – B) ∩ (A – C) ⊂ A – (B ∪ C) …(i) Let y ∈ A – (B ∪ C) ⇒ y ∈ A and y ∉ (B ∪ C) ⇒ y ∈ A and (y ∉ B and y ∉ C) ⇒ (y ∈ A and y ∉ B) and (y ∈ A and y ∉ C) ⇒ y ∈ (A – B) and y ∈ (A – C) ⇒ y ∈ (A – B) ∩ (A – C) ⇒ A – (B ∪ C) ⊂ (A – B) ∩ (A – C) …(ii) We know that, If P ⊂ Q and Q ⊂ P Then, P = Q Therefore, from equations (i) and (ii), A – (B ∪ C) = (A – B) ∩ (A – C) |
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