Hint for Section 10.2 Question 7

7. Recall that a relation R on a set A is symmetric if, and only if, for all x, yA,  if  x R y,  then  y R x.

This question involves an if and only if proof, so you will need to prove the statement in both directions.

Firstly, assume that the relation R is symmetric and prove that R = R^-1.

Secondly, assume that R = R^-1 and prove that R is symmetric.

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