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If A and B are two sets then A ∩ (B ∪ A)c is equal to

If A and B are two sets then A ∩ (B ∪ A)c is equal to Correct Answer ϕ 

Concept:

De morgan's law:

(A ∪ B)c = Ac ∩ Bc

(A ∩ B)c = Ac ∪ Bc

Distributive law in sets:

A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

 

Calculation:

Given: A and B are two sets

To Find: A ∩ (B ∪ A)c

As we know, (A ∪ B)c = Ac ∩ Bc

Therefore (B ∪ A)c = Bc ∩ Ac

Now A ∩ (B ∪ A)c = A ∩ (Bc ∩ Ac)

= (A ∩ Bc) ∩ (A ∩ Ac)             (Using distributive law)

= (A ∩ Bc) ∩ ϕ                        (∵ x ∩ ϕ = ϕ)

= ϕ 

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