Answer
See step by step work for solution
Work Step by Step
We start with $(p \lor q) \rightarrow r$
Use Logical Equivalence: $ ( p \rightarrow q) \equiv (\neg p \lor q)$
$$(p \lor q) \rightarrow r \equiv \neg (p \lor q) \lor r $$
Use De Morgan;s Law:
$$\equiv (\neg p \land \neg q) \lor r $$
Use Distributive Law:
$$\equiv (\neg p \lor r) \land (\neg q \lor r) $$
Use Logical Equivalence: $ ( p \rightarrow q) \equiv (\neg p \lor q)$
$$\equiv (p \rightarrow r) \land (q \rightarrow r) $$
Thus we have derived that $(p \lor q) \rightarrow r$ is logically equivalent to $ (p \rightarrow r) \land (q \rightarrow r) $
