- #1

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## Homework Statement

[itex]R[/itex] is simmetric iff [itex]R=R^{-1}[/itex]

## Homework Equations

[itex]( \forall x \forall y ((x,y) \in R \rightarrow (y,x) \in R)) \leftrightarrow R=R^{-1}[/itex]

## The Attempt at a Solution

My problem is with my formulation in [2.] of the statement I have to prove.

Is that formulation right or the right one is [itex]( \forall x \in A \forall y \in A ((x,y) \in R \rightarrow (y,x) \in R)) \leftrightarrow R=R^{-1}[/itex]?

The difference is significative, at least for my purpose. In the first case, I can prove it, in the second one, I cannot (or I am not able), so I would like to know if the second one is redundant.