Let S denote the set of all functions f- 0-14 - 0- 1- Denote by N the number of functions from S to the set 0- 1- The value of log2log2 N is

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Standard XII

Mathematics

Conditions on the Parameters of Logarithm Function

Let S denote ...

Question

Let S denote the set of all functions f: {0,1} $^{4}$ $\to$ {0, 1}. Denote by N the number of functions from S to the set {0, 1}. The value of log $_{2}$ log $_{2}$ N is ____
16

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Solution

The correct option is A 16
f : {0, 1} $^{4}$ $\to$ {0,1} $\Rightarrow$ S is the set of all functions from a 16 element set to a 2 element set.
|S| = $2^{16}$
N = Number of functions from S to 2 element
set {0, 1} = $2^{2^{16}}$
N = $2^{2^{16}}$
$∴$ log log N = log log $2^{2^{16}}$
= log $2^{2^{16}}$ = 16

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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 log2log2 N is ____16

The correct option is A 16f : {0, 1}4 → {0,1} ⇒ S is the set of all functions from a 16 element set to a 2 element set. |S| = 216 N = Number of functions from S to 2 element set {0, 1} = 2216 N = 2216 ∴ log log N = log log 2216 = log 2216 = 16

Let S denote the set of all functions f: {0,1} $^{4}$ $\to$ {0, 1}. Denote by N the number of functions from S to the set {0, 1}. The value of log $_{2}$ log $_{2}$ N is ____
16