Answer
In case of a bi-conditional statement, it is false only when the simple statements have the different truth value. And when the truth values are either both true or false, then the bi-conditional statement is true.
Example:
Consider the bi-conditional statement,\[p\leftrightarrow q\]. It can be written in statement form as two component statements:
\[p\to q\]is false if p is true and q is false.
\[q\to p\]is false if q is true and p is false.
The only case in which a bi-conditional is true is when the component statements have the same truth value.
The truth table for statement \[\text{ }p\leftrightarrow q\text{ }\]is
It is observed that\[\text{ }p\leftrightarrow q\text{ }\] can be true only when the compound statements have the same truth value, it means either both are true or false.
