A relation R on set A = { ( 1,2,3) is given by R = {( 1,1) , (2,2), (3,3),(1,2),(2,1),(2,3) ,(3,2)}.Show that R is reflexive and symmetric but not transitive .

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Solution

$Since, 1, 2, 3 \in A and (1, 1), (2, 2), (3, 3) \in R that is for each a \in A, (a, a) \in R . So, R is reflexive . We find that ordered pairs obtained by interchanging the components of ordered pairs in R are also in R . So, R is symmetric . We observe that (1, 2) \in R and (2, 3) \in R, but (1, 3) \notin R . So, R is not transitive .$

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