Question

2. Rand S are equivalence relations on a set A then show that Rns on A is also equivalence relation.

JEE/Engineering Exams

Maths

Solution

118

4.0 (1 ratings)

*R aud S will bath contain all (a,a) stype eluments. So, Rns will coutain all (a,a) type So, Rns will be reflexive. * &f R and S bath coutain (a,b): Why will bath contain Cb,al. So, RAS will contain ( (a, b):(b, a) ) So, RAS is syumetric. * Gf RAE COUAGIUS ( (a, b) ;(b, c) ) jit will also coutaiu ( (a, c) ) Jhe saue goes jor S. So, it they both coutain them, RAS will also cautain theus. So, RAS is transihire. So, RAS is equivaleuce relation.