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Thread: 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 $\displaystyle \color{red} need not be}$ 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 $\displaystyle n, m\in \mathbb{Z}$, such that $\displaystyle x=ny$ and $\displaystyle y=mz$. It follows that $\displaystyle x=m\cdot n\cdot z=(mn)\cdot z$, thus x is a multiple of z, i.e. xRz.
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