Proving that $R$ is an equivalence relation.

Question

Let $A$ be the set of all statement forms in three variables $p$, $q$, and $r$. Let $R$ be the relation defined on $A$ as follows: For all $P$ and $Q$ in $A$, $$P\; R\; Q \longleftrightarrow P\; \mbox{and}\; Q\; \mbox{have the same truth table.}$$ Prove that $R$ is an equivalence relation.

Answer 1

equivalence relations have three properties, check them one by one for your 'same truth table' relation