Introduction to Relations (XI) on Sets

Question

Given two finite sets A and B such that $\mathrm{n}\left(\mathrm{A}\right)=2,\mathrm{n}\left(\mathrm{B}\right)=3$. Then total number of relations from A to B is

Easy

Solution

Here $\mathrm{n}(\mathrm{A}\times \mathrm{B})=2\times 3=6$

Since every subset of $\mathrm{A}\times \mathrm{B}$ defines a relation from A to B, number of relation from A to B is equal to number of subsets of $\mathrm{A}\times \mathrm{B}={2}^{6}=64$.

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