In the set Z of all integers,


In the set Z of all integers, which of the following relation R is not an equivalence relation?

(a) $x R y$ : if $x \leq y$

(b) $x R y$ : if $x=y$

(c) $x R y:$ if $x-y$ is an even integer

(d) $x R y:$ if $x \equiv y(\bmod 3)$


(a) $x R y:$ if $x \leq y$

Clearly, $R$ is not symmetric because $x

Hence, (a) is not an equivalence relation.

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