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Equivalence Relation

If 'Q' is the...

Question

If 'Q' is the set of all non-zero rational numbers, $R = {(a, b) / a = \frac{1}{b}}$ is a relation in Q'. Is R an equivalence relation?

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Solution

$a \neq \frac{1}{a}$ so it is not reflexive and hence not an equivalence relative.

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