Show the following is two statements are equivalent without

Show the following is two statements are equivalent without truth tables:

Statement one: -(-p v q)

Statement two: P^-q

Use DeMorgan’s law and double negation.

Solution

Statement one: -( - p V q)

(- - p) ^ (-q) //Using DeMorgan\'s Law ~(P V Q) ~P ~Q

Result: p ^ -q //Using Double negation ~(~P) P

Now Left statement [-( - p V q)] is equal to Right Statement [p ^ -q]

Hence, Statement one: -(-p v q) is equal to Statement two: P^-q