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Math Help - How to prove an equivalence Relation?

  1. #1
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    Lightbulb How to prove an equivalence Relation?

    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.
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  2. #2
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    Re: How to prove an equivalence Relation?

    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.)
    Thanks from smatik
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  3. #3
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    Re: How to prove an equivalence Relation?

    Thanks Bro. Yep it was an easy one..
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