Proof Rules

Question 1

MP

Answer 1

Modus Ponens

p —> q
p
:. q

Question 2

MT

Answer 2

Modus Tollens
p —> q
~q
:. ~p

Question 3

HS

Answer 3

Hypothetical Syllogism
p —> q
q —> r
:. p —> r

Question 4

DS

Answer 4

Disjunctive Syllogism
p v q
~p
\:. ~q
And the opposite

Question 5

CD

Answer 5

Constructive Dilemma
p v q
p —> r
q —> s
\:. r v s

Question 6

Simp

Answer 6

Simplification
p • q
\:. p
Or
p • q
\:. q

Question 7

Conj

Answer 7

Conjunction
p
q
:. p • q

Question 8

Add

Answer 8

Addition
p
\:. p v q
Or
p
\:. q v p

Question 9

DN

Answer 9

Double Negation

p :: ~~p

Question 10

Com

Answer 10

Commutation

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

(p • q) :: (q • p)

Question 11

AS

Answer 11

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

(p • (q • r)) :: ((p • q) • r)

Question 12

DeM

Answer 12

DeMorgan’s Laws
~(p • q) :: (~p v ~q)

~(p v q) :: (~p • ~q)

Question 13

Cont

Answer 13

Contraposition

p —> q) :: (~p —> ~q