Chapter 8 - Equivalence Rules

Question 1

p :: ~~p

Answer 1

Double Negation (DN)

Question 2

(p v q)::(q v p)

p . q)::(q . p

Answer 2

Commutation (Com)

Question 3

(p v (q v r)::((p v q) v r)

p. (q . r)) :: ((p . q) . r

Answer 3

Association (As)

Question 4

~(p.q) :: (~p v ~q)

~(p v q) :: (~p.~q)

Answer 4

De Morgan’s Laws (DeM)

Question 5

(p->q) :: (~q->~p)

Answer 5

Contraposition (Cont)

Question 6

((p.q)->r) :: (p->(q->r))

Answer 6

Exportation (Ex)

Question 7

(p . (q v r))::((p . q) v (p . r))

p v (q . r))::((p v q) . (p v r)

Answer 7

Distribution (Dist)

Question 8

p :: (p . p)

p :: (p v p)

Answer 8

Redundancy (Re)

Question 9

(p q)::((p -> q) . (q -> p))

p q)::((p . q) v (~p . ~q)

Answer 9

Material Equivalence (ME)

Question 10

(p -> q) :: (~p v q)

Answer 10

Material Implication (MI)