<Logical equivalence> means that the two <propositional formulas> receive the same <truth value> under every <Boolean valuation> of the <propositional variables>. Equivalently, $\alpha\leftrightarrow\beta$ is a <tautology>:
$$
\boxed{\forall v\quad v(\alpha)=v(\beta).}
$$

Solution

Past exam of the logic and set theory course of the University of Oxford / 2011 / A / 1 / c / i / Solution

 Solution (source code)