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Reflexive but neither symmetric nor transitive relation Reflexive, symmetric but not transitive relationAn equivalence relation Symmetric but neither reflexive nor transitive relation

Answer :

CSolution :

S=Set of all integers and <br> `R={(a,b), a, b in S and ab ge 0}` <br> For reflexive : `aRaimpliesa.a = a^(2)ge0` <br> for all integers `a.a ge 0` <br> For symmetric : `aRbimpliesabge0AAa, b in S` <br> If `ab ge 0`, then `ba ge 0 implies bRa` <br> For transitive : <br> If `ab ge 0, bc ge 0`, then also `ac ge 0` <br> Relation R is reflexive, symmetric and transitive. Therefore relation is equivalence.