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Math Help - relations help (4)

  1. #1
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    relations help (4)

    hey guys, question:

    Determine whether the following relation is a reflexive, symmetric or transitive. If any is an equivalence relation, describe its equivalence classes.

    xRy iff x is a multiple of y, on

    My answers:

    Is it reflexive? Yes, since x is a multiple of x
    Is it symmetric? No, since if x is a multiple of y, then y is not a multiple of x.
    Is it transitive? IM NOT SURE ABOUT THIS ONE. Any help would be much appreciated.
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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by jvignacio View Post
    hey guys, question:

    Determine whether the following relation is a reflexive, symmetric or transitive. If any is an equivalence relation, describe its equivalence classes.

    xRy iff x is a multiple of y, on

    My answers:

    Is it reflexive? Yes, since x is a multiple of x
    Is it symmetric? No, since if x is a multiple of y, then y \color{red} need not be} a not a multiple of x.
    Is it transitive? IM NOT SURE ABOUT THIS ONE. Any help would be much appreciated.
    Sure, it is transitive because xRy and yRz means that there exist n, m\in \mathbb{Z}, such that x=ny and y=mz. It follows that x=m\cdot n\cdot z=(mn)\cdot z, thus x is a multiple of z, i.e. xRz.
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