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 2 2 N is …

Official answer: 16. Explanation: 1. The domain of each function f is \0, 1\4, which has |\0, 1\4| = 24 = 16 elements. 2. The codomain is \0, 1\, with cardinality 2. 3. The total number of functions from \0, 1\4 to \0, 1\ is: |S| = 216 4. N is the number of functions from S to \0, 1\. Since |S| = 216 and the codomain has size 2, we have: N = 2|S| = 2216 5. Now calculate 2 2 N: 2 N = 2 (2216 ) = 216 2 2 N = 2 (216 ) = 16 Thus, the answer is 16.

Engineering Mathematics · Sets, Relations and Functions

Official IIT answer key · IIT Kharagpur · Audited Aug 2026

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GATE CSE 2014 Set 1 Q50 · NAT · 2 marks

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 _______.

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Sets, Relations and Functions

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How GATE tests Sets, Relations and Functions

In this topic, GATE tests the foundational properties of finite sets, combinatorial counting of structured objects (such as matrices and function spaces), and the existence of mappings (injections, surjections, and bijections). The focus is on comparing cardinalities of constructed sets and understanding how equal or unequal cardinalities govern the existence of specific mapping types.

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Engineering Mathematics · Sets, Relations and Functions

Official IIT answer key · IIT Kharagpur · Audited Aug 2026

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GATE CSE 2014 Set 1 Q50 · NAT · 2 marks

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 _______.

Numerical answer

Enter a value to check

Key concept

Sets, Relations and Functions

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Sets, Relations and Functions

Full Sets, Relations and Functions guide →

More on Sets, Relations and Functions

All 5 questions on Sets, Relations and Functions →

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

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 _______.

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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 _______.

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Let SSS denote the set of all functions f:{0,1}4→{0,1}f: \{0,1\}^4 \to \{0,1\}f:{0,1}4→{0,1}. Denote by NNN the number of functions from SSS to the set {0,1}\{0,1\}{0,1}. The value of log⁡2log⁡2N\log_2 \log_2 Nlog2​log2​N is _______.

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Let SSS denote the set of all functions f:{0,1}4→{0,1}f: \{0,1\}^4 \to \{0,1\}f:{0,1}4→{0,1}. Denote by NNN the number of functions from SSS to the set {0,1}\{0,1\}{0,1}. The value of log⁡2log⁡2N\log_2 \log_2 Nlog2​log2​N is _______.

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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 _______.

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 _______.