Q.10 Give an example of a relation.

(iv) Which is Reflexive and transitive but not symmetric.

Answers (1)

Let there be a relation R in R

R=\left \{ (a,b):a\leq b \right \}

(a,a)\in R  because a=a

Let (a,b)\in R  i.e.a\leq b

But (b,a)\notin R i.e.b\nleqslant a

So it is not symmetric.

Let (a,b)\in R  i.e.a\leq b   and (b,c)\in R  i.e. b\leq c

This can be written as a\leq b\leq c  i.e. a\leq c  implies (a,c)\in R

Hence, it is transitive.

Thus, it  is Reflexive and transitive but not symmetric.

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