“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

$A⟺B≡((A⟹B)∧(B⟹A))$