The number of relations R from an m-element s | vedclass

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(A) The given condition $(a, b_1) \in R$ and $(a, b_2) \in R \Rightarrow b_1 = b_2$ is the definition of a function from set $A$ to set $B$.In a funct

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$n^m$

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(A) The given condition $(a, b_1) \in R$ and $(a, b_2) \in R \Rightarrow b_1 = b_2$ is the definition of a function from set $A$ to set $B$.In a function,every element $a \in A$ must be mapped to exactly one element $b \in B$.Since there are $m$ elements in set $A$ and each element has $n$ choices in set $B$,the total number of such relations (which are functions) is $n 	imes n 	imes \dots 	imes n$ ($m$ times).Therefore,the total number of such relations is $n^m$.

The number of relations $R$ from an $m$-element set $A$ to an $n$-element set $B$ satisfying the condition $(a, b_1) \in R, (a, b_2) \in R \Rightarrow b_1 = b_2$ for $a \in A, b_1, b_2 \in B$ is

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