Chapter 0.1, Problem 9E

On page 4 of the text, we stated as more or less “obvious” the fact that (*) $p\leftrightarrow q$ is true if $p$ and $q$ have the same truth values and false if $p$ and $q$ have different truth values.

Using the fact that $p\leftrightarrow q$ means “ $p\to q\text{and}q\to p$” together with how the truth values for $x\to y$ are determined, write a short note (in good English) explaining why (*) is the case.