July 24, 2021
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.