How do i answer this discrete maths Problem?

Question

Using logical equivalencies prove that (p∧q)→(p∨q) is a tautology. (No truth tables)

Answer 1

~(p ^ q) y ( p v q) = <--- identity for inference: A-->B = ~A v B

~p v ~q v p v q = <--- DeMorgans

~p v p v ~q v q <---- commutative

(~p v p) v (~q v q) <--- associative

T v T <--- x or not x must be true

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