Simplying a Boolean Expression

Question

Hey everyone can anyone help me in simplifying the following boolean expression with explanation?

\begin{equation}[((p\land q)\implies r)\implies((q\land r')\implies r')]\land[(p \land q)\implies(q\iff p)]\end{equation}

Answer 1

Based on the following table, the given statement is always true for any $p,q,r$:

Answer 2

Note that $(q\land r')\implies r'$ is always true. Thus first part of the statement becomes trivial. Consider the statement $(p \land q)\implies(q\iff p)$. If $p=q=1$, it is true, otherwise it is vacuous. Hence, both parts of the to-be-simplified statement are always true and hence it is a tautology.