Project ForgeDiscrete Mathematics
Set Theory & Abstract Algebra
GATE 2014
Hard
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
16
Explanation
|S| = number of functions from a 2⁴=16-element domain to a 2-element codomain = 2^16 = 65536. N = number of functions from S to {0,1} = 2^|S| = 2^65536. So log₂N = 65536 = 2^16, and log₂log₂N = 16.
Source: GATE CS 2014 (Session 1) (2014)
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