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# $p\leftrightarrow q$ is equivalent to

$\begin{array}{1 1}(1)p\to q&(2)q\to p\\(3)(p\to q)\vee(q\to p)&(4)(p\to q)\wedge (q\to p)\end{array}$

Truth table for $p \leftrightarrow q$
Truth table for $p \to q$
Truth table for $q \to p$
Truth table for $(p \to q) \vee (q \to p)$
Truth table for $(p \to q) \wedge (q \to p)$
The last column of the truth table for $p \leftrightarrow q$ and $(p \to q) \wedge (q \to p)$ are identical.
Statement $p\leftrightarrow q$ and $(p\to q)\wedge (q\to p)$ are equivalent