Question

If A,B and C are any three sets, then prove that : A - (B∩C)=(A-B)U(A-C)

Answer 1

here is your answer

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Answer 2

Answer:

The proof is explained step wise below :

Step-by-step explanation:

Let x be any element of A - (B ∩ C). Then, x ∈ A - (B ∩ C)

⇒ x ∈ A and x ∉ (B ∩ C)

⇒ x ∈ A and (x ∉ B or x ∉ C)

⇒ (x ∈ A and x ∉ B) or (x ∈ A and x ∉ C)

⇒ x ∈ (A - B) or x ∈ (A - C)

⇒ x ∈ (A - B) ∪ x ∈ (A - C)

∴ A - (B ∩ C) ⊆ (A - B) ∪ (A - C)

Similarly, (A - B) ∪ (A - C) ⊆ A - (B ∩ C)

Hence, A - (B ∩ C) = (A - B) ∪ (A - C)