Question

R={(a,a),(b,b),(c,c),(a,b),(a,c),(b,a),(c,a)} find is it equivalence or not

Answer 1

Answer:

No there is no equivalence

Step-by-step explanation:

.

R is reflexive: If a∈X, aRa since (a,a)∈R.

R is symmetric: If a,b∈X, then (a,b)∈R⇔(b,a)∈R.

R is not transitive: If a,b,c∈X, then aRb and bRc implies aRc. But (b,c) is not an element of R and (a,c) is not an element of R.

So R is not an equivalence  For transitivity should a≠b≠c