Question

use De Morgan's laws to determine whether the two statements are equivalent ~p v ~q, ~(p ^ q)

Answer 1

Do you want to use truth table to prove the De Morgan's laws or just to answer yes or no because the given is part of the De Morgan's laws.
~(p v q) <=> ~p ^ ~q
~(p ^ q) <=> ~p v ~q

Answer 2

the truth table to prove the de morgan's laws

Answer 3

p q p v q ~(p v q) ~p ~q ~p ^ ~q

T T T F F F F
T F T F F T F
F T T F T F F
F F F T T T T

Answer 4

You will prove your problem in a similar way using the truth tables of the OR and AND statements.
p q p v q p ^ q
T T T T
T F T F
F T T F
F F F F