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given a relation on R on the set A={1,2,3,4} in the form of matrix representation as ,

$M_R$=$\begin{bmatrix} 0 & 1 & 0 & 0\\ 0& 0& 1 &0 \\ 0& 0& 0 &1 \\ 0& 0& 0& 0 \end{bmatrix}$

Then the cardinality of the smallest equivalence relation on A which contains R is equal to

answer given-16
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Given adjacency from the matrix:

(1,2) (2,3) (3,4)

to satisfy reflexive: adding (1,1) (2,2) (3,3) (4,4)

to satisfy symmetric: adding (2,1) (3,2) (4,3)

to satisfy transitive: adding (1,3) (2,4) (4,2) (3,1) (1,4) (4,1)

Hence, the cardinality is 16

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