Answer to Question #75995 in Discrete Mathematics for Amrutha Ginkala

Question

X be a non-empty set and let R be an equivalence relation on X. For each x ∈ X, define
[x]={y∈X suchthatxRy}
to be the equivalence class of x. Here x R y means (x, y) ∈ R.
SupposethatA=[x]andB=[y]. ProvethatifA∩B̸=∅,thenA=B.