Question

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 log₂ log₂ N is ______.

Answer 1

Concept:

Let A and B are two sets having m and n elements respectively.

In f : A → B, total number of functions will be n^m.

Explanation:

S -> f : 2⁴ → 2 gives total number of functions to be 2^{2^4} = 2¹⁶

N is defined by f : S-> {0,1}.

Therefore, total number of functions will be 2^S

Hence, log₂ log₂ N

= log₂ log₂ 2^S

= log₂ log₂ 2^{2^16}

= log₂2¹⁶

= 16