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Equivalence Relations

  1. Mar 4, 2010 #1
    1. The problem statement, all variables and given/known data

    I need a little help in understand this question:

    Let E and F be two sets, R a binary relation on the set E and S a binary relation on the set F. We define a binary relation, denoted RxS, on the set ExF in the following way ("coordinate- wise"):
    (a,b) (RxS) (c,d) <--> aRc and bSd.
    If R and S are equivalence relations, prove that RxS is an equivalence relation.

    2. Relevant equations

    3. The attempt at a solution

    I said aRc => (a,c) and bSd=> (b,d)

    I assumed that aRc and bSd are from ExF.
    I'm not sure that what I am doing is right
  2. jcsd
  3. Mar 4, 2010 #2


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    ExF is the set of ordered pairs (x,y) where x is in E and y is in F. You have (a,b) and (c,d) are elements in ExF, so this means a and c are elements of E while b and d are elements of F.

    To show that RxS is an equivalence relation, you need to show it satisfies three properties: reflexivity, symmetry, and transitivity.

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