The number of reflexive relations on a set wi | vedclass

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(D) relation $R$ on a set $A$ with $n$ elements is reflexive if $(a, a) \in R$ for every $a \in A$.There are $n^2$ total possible ordered pairs in the

Vedclass · Accepted Answer

$2^{12}$

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(D) relation $R$ on a set $A$ with $n$ elements is reflexive if $(a, a) \in R$ for every $a \in A$.There are $n^2$ total possible ordered pairs in the Cartesian product $A 	imes A$.For a relation to be reflexive,all $n$ elements of the form $(a, a)$ must be present in the relation.The remaining $n^2 - n$ ordered pairs can either be in the relation or not,giving $2^{n^2 - n}$ possibilities.For a set with $n = 4$ elements,the number of reflexive relations is $2^{4^2 - 4} = 2^{16 - 4} = 2^{12}$.

The number of reflexive relations on a set with $4$ elements is equal to

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