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

$$\begin{array}{ccc}A& B& A⟺B\\ T& T& T\\ T& F& F\\ F& T& F\\ F& F& T\end{array}$$

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

Remarks

$A⟺B\equiv ((A⟹B)\wedge (B⟹A))$