Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

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Solution

The given relation R in the set {1,2,3} is defined as R={( 1,2 ),( 2,1 )}.

( 1,1 )∉R. Hence, R is not reflexive.

( 1,2 )∈R and ( 2,1 )∈R. Hence, Ris symmetric.

( 1,2 ) and ( 2,1 )∈R, but ( 1,1 )∉R. Hence Ris not transitive.

Therefore, the given relation R={( 1,2 ),( 2,1 )} in set {1,2,3} is symmetric but neither reflexive, nor transitive.

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