AMU Engineering 2018 solved paper Solved Paper

We know that the union of two equivalence relation on a set is not necessarily an equivalence relation on the set.
For example let x={a,b,c}
R={(a,a),(b,b)(c,c),(a,b),(b,a)}
S={(a,a),(b,b),(c,c),(b,c),(c,b)}
Clearly, R and S are equivalence relation.
But R∪S is not transitive because (a,b)∈R∪S and (b,c)∈R∪S but (a,c)∉R∪S
Hence, R∪S is not equivalence relation.