I am having problem solving this question.
Let f:X->Y be a function. Define a relation R on X given be R={(a,b):f(a)=f(b)}. Show that R is an equivalence Relation.
This question is from CBSE (India) Board.
Well, it helps to know what an equivalence relation is!
aRb, on set X, is an equivalence relation if and only if it
1) is reflexive: aRa for every a in X. Is it true that f(a)= f(a) for all a in X?
2) is symmetric: if aRb then bRa. Is it true that if f(a)= f(b) then f(b)= f(a)?
3) is transitive: if aRb and bRc then aRc. Is it true that if f(a)= f(b) and f(b)= f(c) then f(a)= f(c)?
(This is an easy problem because it involves "=" and "=" is the epitome of equivalence relations.)