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GATE | GATE-CS-2014-(Set-1) | Question 60

Let S denote the set of all functions f: {0,1}4 -> {0,1}. Denote by N the number of functions from S to the set {0,1}. The value of Log2Log2N is ______.
(A) 12
(B) 13
(C) 15
(D) 16

Answer: (D)
Explanation: 

The given mapping S is defined by f:{0,1}^4 -> {0,1} .
So, number of functions from S will be 2^16.
Now N is defined by f : S-> {0,1}.
So Number of functions from S to {0,1} will be 2^S.
Hence log2log2N = log2S = 16

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