Given, $F_1 \wedge F_2 \implies F_3$ is $True$.
$F_1 \wedge F_2 \implies \neg F_3$ is $True$.
Notice that, the antecedent is same for both the statements but the conclusion is different. Whenever $F_3$ is $True$, then $\neg F_3$ is $False$ and vice-versa. So, for both the statements to be tautology the antecedent is the defining proposition. So, antecedent needs to be $False$, so as to predict $True$ for both the statements. Thus, $F_1 \wedge F_2$ is $False$, i.e, $Not$ $Satisfiable$.
Thus, option B is correct.