Let relation is defined on set s={a,b,c}
Let R1={(a,a),(b,b),(c,c),(a,b),(b,a)}
And let. R2={(a,a),(b,b),(c,c),(b,c),(c,b)}
Here both are equivalence relation
But R1UR2={(a,a),(b,b),(c,c),(a,b),(b,a),(b,c),(c,a)}
Now here it can be seen that (a,c) is not pre sent in R1UR2 as it should be to make it transitive since (a,b) and (b,c) is present.