~(p or q) or (~p & q) = ~p?

Question

Prove the above logical equivalence using the laws of logic also state the laws their detail to understand for a new one with each statement form, please. (this is question of discrete math)

Answer 1

I'll use v (Latin "vel") for "or."

~(p v q) v (~p & q) ...........given
(~p & ~q) v (~p & q) ........DeMorgan
~p & (~q v q) ..................distribution
~p .........................simplification

Answer 2

Distributive sources. p^2- pq -q^2 + pq observe the final term is beneficial because of the fact -q * -p makes a beneficial pq. team like words. p^2 - q^2 - pq + pq the two pq words cancel. you have: p^2 - q^2 A.