Official solution
Given q is F and (p \[ \wedge \] q) \[ \leftrightarrow \] r is T
\[ \Rightarrow \] p \[ \wedge \] q is F which implies that r is F
\[ \Rightarrow \] q is F and r is F
\[ \Rightarrow \] (p \[ \wedge \] r) is always F
\[ \Rightarrow \] (p \[ \wedge \] r) \[ \to \] (p \[ \vee \] r) is tautology.