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## Homework Statement

In Velleman's "How to Prove it", he gives a proof that "R is symmetric iff R = R

^{-1}, which I find to be confusing when he is proving that [tex]R^{-1}\subseteq{R}[/tex]:

Now suppose [tex](x,y)\in R^{-1}[/tex]. Then [tex](y,x)\in R[/tex], so since R is symmetric, [tex](x,y)\in R[/tex]. Thus, [tex]R^{-1}\subseteq R[/tex] so R=R

^{-1}

It seems to me that he is saying that since [tex]xRy\rightarrow yRx[/tex] and yRx, xRy, which makes no sense.

Basically my question is this: how this part of his proof could be correct?

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