A relation $S$ is an equivalence relation if and only if $S$ is
symmetric and transitive and reflexive
transitive and symmetric and associative
symmetric and composite and intransitive
transitive and antireflexive and symmetric
None of these

What is Antireflexive?

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Consider the relation $S$ on the set {$a,b,c$} given by

$S =$ { $(a,a),(a,b),(b,a),(b,b),(c,c),(b,c),(c,b)$ }

i. Prove $S$ is reflexive.

ii. Prove $S$ is symmetric.

iii. Show $S$ is not an equivalence relation.

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