If A = {1, 2, 3, dots, m},then the total numb | vedclass

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(A) relation $R$ on a set $A$ is reflexive if $(a, a) \in R$ for all $a \in A$. Given set $A$ has $m$ elements,so the Cartesian product $A 	imes A$ h

Vedclass · Accepted Answer

$2^{m^2 - m}$

Vedclass · Answer

(A) relation $R$ on a set $A$ is reflexive if $(a, a) \in R$ for all $a \in A$. Given set $A$ has $m$ elements,so the Cartesian product $A 	imes A$ has $m^2$ elements. For a relation to be reflexive,it must contain all $m$ diagonal elements of the form $(1, 1), (2, 2), \dots, (m, m)$. The remaining elements in $A 	imes A$ are $m^2 - m$. Each of these $m^2 - m$ elements can either be present or absent in the relation. Therefore,the total number of reflexive relations is $2^{m^2 - m}$.

If $A = \{1, 2, 3, \dots, m\}$,then the total number of reflexive relations that can be defined from $A \to A$ is:

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