Using the laws of propositions of algebra, $(P\rightarrow(Q\vee\sim R))\rightarrow(P\wedge Q)$ simplifies to:

1. Replace the inner conditional using $A\rightarrow B\equiv\;\sim A\vee B$: the antecedent becomes $\sim P\vee(Q\vee\sim R)$. 2. Apply the same rule to the outer conditional, negating that whole antecedent. 3. De Morgan's law turns $\sim(\sim P\vee Q\vee\sim R)$ into $P\wedge\sim Q\wedge R$. 4. The statement is now $(P\wedge\sim Q\wedge R)\vee(P\wedge Q)$, and $P$ factors out. 5. The bracket $(\sim Q\wedge R)\vee Q$ absorbs to $Q\vee R$, leaving $P\wedge(Q\vee R)$. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/2, Question 2: Logic_