“A if and only if B”, written symbolically as $A⟺B$, is defined by the truth table:

\hline A & B & A \iff B\\ \hline T & T & T\\ T & F & F\\ F & T & F\\ F & F & T\\ \hline \end{array}

Thus, $A⟺B$ is only true when $A$ and $B$ have the same truth values.

Remarks §

$A⟺B\equiv ((A⟹B)\wedge (B⟹A))$