USE THE TRUTH TABLE TO SHOW THE MORGAN’S LAW
DE Morgan’s law
THERE ARE TWO WAYS OF SOLVING DE MORGAN’S LAW ON TRUTH TABLE
EITHER ~[pVq] = ~p^ ~q
OR ~ [p^q]= ~pv ~q
USING THE FIRST ONE TO PROVE DE MORGAN’S LAW i.e
~[pVq]= ~p^ ~q
| P | Q | ~p | ~Q | PVq | ~[pVq] | ~p^~ q |
| T | T | F | F | T | F | F |
| T | F | F | T | T | F | F |
| F | T | T | F | T | F | F |
| F | F | T | T | F | T | T |
OR ~[p^q] = ~pv~q
| P | Q | ~p | ~Q | P^q | ~[p^q] | ~pv~ q |
| T | T | F | F | T | F | F |
| T | F | F | T | F | T | T |
| F | T | T | F | F | T | T |
| F | F | T | T | F | T | T |
It is logically equivalent.
NOTE: IN EIITHER WAY IT MUST PROVE THAT THE LEFT HAND SIDE IS LOGICALLY EQUIVALENT WITH THE RIGHT HAND SIDE.
