GATE | GATE-CS-2003 | Question 37

Let f : A → B be an injective (one-to-one) function.

Define g : 2A → 2B as :
g(C) = {f(x) | x ∈ C}, for all subsets C of A.
Define h : 2B → 2A as :
h(D) = {x | x ∈ A, f(x) ∈ D}, for all subsets D of B. 

Which of the following statements is always true ?
(A) g(h(D)) ⊆ D
(B) g(h(D)) ⊇ D
(C) g(h(D)) ∩ D = ф
(D) g(h(D)) ∩ (B – D) ≠ ф

Answer: (A)
Explanation:
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