Given that the truth value of $\left(p\wedge q\right)\to \left(~q\vee r\right)$ is $F$ .

For the above truth value to be possible, $\left(p\wedge q\right)$ should be TRUE and $\left(~q\vee r\right)$ should be FALSE.

$\left(p\wedge q\right)$ is TRUE when $p \& q$ both are TRUE.

$\left(~q\vee r\right)$ is FALSE when $q$ is TRUE and $r$ is FALSE.

So, the truth values of $p, q, r$ are $T, T, F$ respectively.