Question

Let X be a nonempty set and let P(X) denote the collection of all subsets of X. Define

f : X × P(X) → R by

f(x,A) = {1, if x∈ A, 0, if x ∉ A

Then f (x, A ∪ B) equals -

(A) f (x, A) + f (x, B)

(B) f (x, A) + f (x, B) – 1

(C) f (x, A) + f (x, B) – f (x, A) f (x, B)

(D) f (x, A) + | f (x, A) – f (x, B)|

Answer 1

Correct Option :- (C) f (x, A) + f (x, B) – f (x, A) f (x, B)

Explanation :-