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Math Help - equivalence relation

  1. #1
    MHF Contributor chiph588@'s Avatar
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    equivalence relation

    Which of the following relations is an equivalence relation?
    (a) {(1, 1), (2, 2), (3, 3), (1, 2)}
    (b) {(a, b) | (a = b) v (a is odd ^ b is even)}
    (c) {(x, y) | x + y is even}
    (d) {(t1, t2) | t1 and t2 are triangles, and some angle in t1 is equal to some angle in t2}

    I know the answer is (c), but my question is how do you even work on (a) when it's just a list of points?
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  2. #2
    Senior Member vincisonfire's Avatar
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    I guess that by (1,1) they mean 1 related to 1, (2,2) 2 related to 2, etc.
    As for c) as I understand it you have x related to y if x+y is even.
    Of course x is related to himself because 2x is even.
    If x is related to y then y is related to x because of the commutativity of addition (I guess you work in N Z Q or R).
    If x is related to y and y related to z then x is not necessarily related to z. Think of the case where you have three odd numbers.
    Maybe I made a stupid mistake but does that make sense to you?
    As for d, a triangle is related to itself because it has the same angles.
    The relation is also symmetric but not transitive.
    It may be b) but I don't really understand your notation.
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