Relations

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If R is a relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B is

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$2^{(} mn)$

$2^{(} m + n)$

$m^{n}$

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Subject: mathematics
Chapter: sets, relations and functions
Topic: relations
Difficulty: Medium
Year: 2025

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Correct Answer:

$2^{(} mn)$

Determine Product size: The Cartesian product $A \times B$ consists of all ordered pairs $(a_{i}, b_{j})$ . There are $m \times n = mn$ such pairs.
Identify Relation: Any relation $R$ is a subset of $A \times B$ .
Subset Counting: For a set with $N$ elements, there are $2^{N}$ possible subsets.
Formula: Let $N = mn$ . Total relations = $2^{mn}$ .

This medium difficulty mathematics question is from the chapter sets, relations and functions, covering the topic of relations. It appeared in the 2025 exam.

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