Question

construct the truth table

1. (~p v q) -> ~ q

2. (p ^ ~ q ) <--> ( q v r )

3. [(p v q) v (~p ^ q) -> r​

Answer 1

Answer:

p->q = ~pvq Def. of implication

p<->q = (p->q)(q->p) Def. of equivalence

p(+)q = ~pq v p~q Def. of ex-or

~(~p) = p Double negation

~T = F ~F = T Def. of negations

pvq = qvp pq = qp Commutative laws

(pvq)vr = pv(qvr) p(qr) = (pq)r Associative laws

p(qvr) = pq v pr pv(qr) = (pvq)(pvr) Distributive laws

pvF = p pT = p Identity laws

pv~p = T p(~p) = F Negation laws

pvp = p pp = p Idempotent laws

~(pvq) = (~p)(~q) ~(pq) = ~pv~q DeMorgan's laws

pvT = T pF = F Universal bound laws

pv(pq) = p p(pvq) = p Absorption laws

pv(~pq) = pvq p(~pvq) = pq " "