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I'm studying for my final exam of discrete mathematics, is an exercise in particular concerning equivalence relations do not know how to start:

$$ \text{Let } A = \left\{{3, 5, 6, 8, 9, 11, 13}\right\}\text{ and } R \subseteq A\times A: xRy\Longleftrightarrow{ x \equiv y}$$

How I can prove the symmetry, reflexivity and transitivity?

  • $(1)$ symmetry ($xRx$ for any $x$),

  • $(2)$ reflexivity ($xRy$ implies $yRx$), and

  • $(3)$ transitivity ($xRy$ and $yRz$ implies $xRz$)

I know clearly that the properties must be satisfied by other exercises I've done, but this one in specific, I do not know how to prove mathematically

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    what is the $x$ triple-bar $y$?2012-06-07
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    @ncmathsadist exactly equal or equivalent2012-06-07
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    These then follow because equality is an equivalence relation on any set.2012-06-07
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    Use \LaTeX to post, not an image. You have problems here and I can't edit the image.2012-06-07
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    What's A2? From your question, I presume it's the cartesian product of _A_ with itself, so what's _A_?2012-06-07
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    @RickDecker yes is the cartesian product of A x A2012-06-07
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    @ncmathsadist I don´t know how to post in \LaTeX2012-06-07
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    @Melkhiah66 That just leaves the question of what _A_ is.2012-06-07
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    @RickDecker Sorry...my bad...question edited2012-06-07

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