Symmetric and transitive but not reflexive. - Vidyadip

Question

Symmetric and transitive but not reflexive.

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Answer

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

It is clear that $\text{x}\geq\text{x}$	$\therefore$	R is reflexive.
It is clear that x is not the brother of x.	$\therefore$	R is not symmetric.
Also if x is brother of y and y is brother of z then
x can be brother of z	$\therefore$	R is transitive.

Therefore, R is symmetric and transitive but not reflexive.

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