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The question is: Let S be a set, R be a binary relation on S, and x an element of S. Express in English the negation of the statement “For all x in S, xRx”.

I was originally thinking since the negation is just the opposite, I would switch S and R to get an expression of "For all x in R, xSx"

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2 Answers

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"There exists an $x$ in $S$ such that $(x,x) \not\in R$ "

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I would go with:

"There exists an element $x$ in the set $S$, such that $x$ is not related to itself under $R$."

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