The statement pattern $p\wedge \left(~p\wedge q\right)$ is

Which of the following statement pattern is a tautology?

$S_1\equiv \left(~q\wedge p\right)\wedge q$

$S_2\equiv \left[p\wedge \left(p\to q\right)\right]\to q$

$S_3\equiv \left(p\wedge q\right)\wedge \left(~p\vee ~q\right)$

$S_4\equiv \left(p\wedge q\right)\to r$

Which of the following statement pattern is a tautology?

$S_1\equiv ~p\to \left(q\leftrightarrow p\right)$

$S_2\equiv ~p\vee ~q$

$S_3\equiv (p\to q)\wedge \left(q\to p\right)$

$S_4\equiv \left(q\to p\right)\vee \left(~p\leftrightarrow q\right)$