Question

Prove that there is only one relation in {1,2,3} which is reflexive and symmetric but not transitive and which contains (1, 2) and (1, 3).

Answer 1

A={1,2,3}
R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1)}
Here R is reflexive because (a,a) belongs to R that is {(1,1),(2,2),(3,3)} belongs to R
Similarly,R is symmetric because (a,b)belongs to R=(b,a)belongs to R that is {(1,2),(2,1),(1,3),(3,1)}belongs to R
But R is not transitive because {(2,3)} does not belong to R.
Hence,it is proved.