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GATE | GATE-CS-2001 | Question 28

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  • Last Updated : 28 Jun, 2021
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Let f: A→B be a function, and let E and F be subsets of A. Consider the following statements about images.

S1: f (E ∪ F) = f (E) ∪ f (F)
S1: f (E ∩ F) = f (E) ∩ f (F) 

Which of the following is true about S1 and S2?
(A) Only S1 is correct
(B) Only S1 is correct
(C) Both S1 and S2 are correct
(D) None of S1 and S2 is correct

Answer: (A)

Explanation: S1 : correct, because both L.H.S. and R.H.S. will contain exactly the images of all elements in E and F.
S2 : false, let f is a constant function s.t. range is only {1}. Now let E and F be two partitions of set A, then clearly A ∩ B is φ, and so f (φ) is not defined, but f (E) ∩ f (F) is {1}.
So S1 is true, but S2 is false. So option (A) is correct.


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