Correct option (D) 3n
Let A = { a1 , a2 , a3 , …, an }. For ai ∈ A, we have the following choices:
(i) ai ∈ P and ai ∈ Q
(ii) ai ∈ P and ai ∉ Q
(iii) ai ∉ P and ai ∈ Q
(iv) ai ∉ P and ai ∉ Q
Out of these, only (ii), (iii) and (iv) imply ai ∉ P∩Q. Therefore, the number of ways in which none of a1 , a2 , …, an belong to P ∩ Q is 3n .