Let $F_1\left(A,B,C\right)=\left(A\wedge ~B\right)\vee \left[~C\wedge \left(A\vee B\right)\right]\vee ~A$ and $F_2\left(A,B\right)=\left(A\vee B\right)\vee \left(B\to ~A\right)$ be two logical expressions. Then :

Given the following two statements:

$\left(S_1\right):\left(q\vee p\right)\to \left(p\leftrightarrow ~q\right)$ is a tautology
$\left(S_2\right):~q\wedge \left(~p\leftrightarrow q\right)$ is a fallacy. Then :

Contrapositive of the statement :

'If a function $f$ is differentiable at $a$, then it is also continuous at $a$', is