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Math Help - relations help (3)

  1. #1
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    relations help (3)

    Let A = {1,2,4,5,6,8,11,13,15,17,153}. Define a relation R on A by writing (x,y) \epsilon R iff x - y is a multiple of 5.

    a) Show that R is an equivalence on A.

    My answer:
    Is it reflexive? Yes, since x-x = 5 \cdot 0, 0 \epsilon \mathbb{Z}
    Is it symmetric? No, since x-y = 5k but y-x = -5k, k \epsilon \mathbb{Z}

    Is this reflexive and symmetric ones correct? thanks
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  2. #2
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    Quote Originally Posted by jvignacio View Post
    Is it symmetric? No, since x-y = 5k but y-x = -5k, k \epsilon \mathbb{Z}
    -5k=5(-k) and k is integer. (In other words, -5k is a multiple of 5, too.)
    So it is reflexive.
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  3. #3
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    Quote Originally Posted by kompik View Post
    -5k=5(-k) and k is integer. (In other words, -5k is a multiple of 5, too.)
    So it is reflexive.
    Yep thats right forgot integers are minus numbers aswell.
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