Solution to Prove the logical equivalence of the following statements, ~(p V ~q) V (~p ^ ~q) … - Sikademy

Oct. 28, 2020

Archangel Macsika Sikademy Image

Archangel Macsika

Prove the logical equivalence of the following statements, ~(p V ~q) V (~p ^ ~q) ≡ ~p

Solution for ~(p V ~q) V (~p ^ ~q) ≡ ~p

~(p V ~q) V (~p ^ ~q) ≡ ~p
1(~p ^ ~(~q)) V (~p ^ ~q)(De Morgan’s law)
2(~p ^ q) V (~p ^ ~q)(Double negative law)
3~p ^ (q V ~q)(Distributive law)
4~p ^ t(Negation law)
5~p(Identity law)

Hence proved.

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