As $\left( {p \wedge q} \right) \leftrightarrow r$ is true

$\therefore $ If ${p \wedge q}$ is true and $r$ is true.       or       ${p \wedge q}$ is $F$ and $r$ is $F$ .

As $q$ is false

${p \wedge q}$ can not be true

This case is not possible

$\therefore $ Their will be two cases for $p,q,r$.

$T,F,F,$ or $F,F,F$ respectively