UPSC NDA I 2014 Mathematics Paper

S= Set of all integers and R={(a,b),a,b∈S and ab≥0}
For reflexive:
aRa=a⋅a=a2≥0, so it's reflexive.
For symmetric:
aRb=ab≥0 and bRa=ba≥0, So relation is symmetric
For transitive:
For all integers a⋅a≥0. If ab≥0,bc≥0, then also ac≥0
So, Relation Is reflexive, symmetric and transitive. Therefore relation is equivalence.