Reflexive and symmetric but not transitive. - Vidyadip

Question

Reflexive and symmetric but not transitive.

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Answer

“is friend of” R = {( x, y) : x is a friend of y}

It is clear that x is friend of x.	$\therefore$	R is reflexive.
Also x is friend of y and y is friend of x.	$\therefore$	R is symmetric.
Also if x is friend of y and y is friend of z then
x cannot be friend of z.	$\therefore$	R is not transitive.

Therefore, R is reflexive and symmetric but not transitive.

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