Use laws of logical equivalence to verify the logical equivalence for the statements

Question

Use laws of logical equivalence to verify the logical equivalence for the statements. (do not use truth tables!) Justify each step:

𝑝 → 𝑞 ∨ 𝑟 ≡ 𝑝 ∧ ~𝑞 → r

Please show me every step and explain it so that I can understand it.

Answer 1

p --> (q or r) is given

~p or (q or r) by implication theorem

(~p or q) or r by associative property

~(p and ~q) or r by demorgan's law

(p and ~q) -->r by implication theorem