Answer
See step by step work for solution
Work Step by Step
We start with $p→(q∨r)$
Use Logical Equivalence: $(p→q)≡(¬p∨q)$
$$p→(q∨r)≡¬p∨(q∨r)$$
Use Idempotent Law:
$$≡(¬p∨¬p)∨(q∨r)$$
Use Associative and Commutative Law:
$$≡(¬p∨q)∨(¬p∨r)$$
Use Logical Equivalence:$(p→q)≡(¬p∨q)$
$$≡(p\rightarrow q)∨(p\rightarrow r)$$
We have thus derived that $p→(q∨r) \equiv (p\rightarrow q)∨(p\rightarrow r) $
