Let A = {1,2,3,4,5} Let R = {(1,1), (1,2),(2,1),(2,2),(3,3),(3,4),(4,3),(4,4),(5,5)} and

S = {(1,1)(2,2),(3,3),(4,4),(4,5),(5,4)(5,5)} be the relation on A. Find the smallest equivalence relation containing the relation R and C.

Solution: Let A = {1,2,3,4,5}

R = {(1,1)(1,2),(2,1),(2,2),(3,3),(3,4),(4,3),(4,4),(5,5)}

S = {(1,1)(2,2),(3,3),(4,4),(4,5),(5,4)(5,5)}

$\therefore$ $M_R = \begin{matrix} \Bigg [1 1 0 0 0 …