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Math Help - equalvalence relation

  1. #1
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    Question equalvalence relation

    Let X be the set {1,2,3,4} and let R={(1,1),(1,2),(2,1),(2,2),(3,3),(3,4),(4,3),(4,4) }. Show that R is an equaivalence relation and write down its equvalence classes.

    I don't really understand what does equivalence relation mean.
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  2. #2
    Senior Member tukeywilliams's Avatar
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    An equivalence relation is reflexive, transitive, and symmetric.
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    that's what I don't understand about.
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by r7iris View Post
    Let X be the set {1,2,3,4} and let R={(1,1),(1,2),(2,1),(2,2),(3,3),(3,4),(4,3),(4,4) }. Show that R is an equaivalence relation and write down its equvalence classes.

    I don't really understand what does equivalence relation mean.
    Quote Originally Posted by tukeywilliams View Post
    An equivalence relation is reflexive, transitive, and symmetric.
    Reflexive: aRa ~ \forall a \in R

    Transitive: \text{If} ~ aRb ~ \text{and} ~ bRc \implies aRc ~ \forall a,b,c \in R

    Symmetric: aRb \implies bRa ~ \forall a,b \in R

    For example, this relation is reflexive because 1R1, 2R2, 3R3, 4R4. (As can be seen by noting that \{ (1, 1), (2, 2), (3, 3), (4, 4) \} \in R.)

    You can show that it is symmetric because 1R2 and 2R1, etc. ( \{ (1, 2), (2, 1) \} \in R) Note that we need not require that 3R1 because (1, 3) is not in the set R.

    I'll leave transitivity to you (that's the long one and I'm lazy. )

    -Dan
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