Proof Rules Flashcards
1
Q
MP
A
Modus Ponens
p —> q
p
:. q
2
Q
MT
A
Modus Tollens
p —> q
~q
:. ~p
3
Q
HS
A
Hypothetical Syllogism
p —> q
q —> r
:. p —> r
4
Q
DS
A
Disjunctive Syllogism p v q ~p \:. ~q And the opposite
5
Q
CD
A
Constructive Dilemma p v q p —> r q —> s \:. r v s
6
Q
Simp
A
Simplification p • q \:. p Or p • q \:. q
7
Q
Conj
A
Conjunction
p
q
:. p • q
8
Q
Add
A
Addition p \:. p v q Or p \:. q v p
9
Q
DN
A
Double Negation
p :: ~~p
10
Q
Com
A
Commutation
(p v q) :: (q v p)
(p • q) :: (q • p)
11
Q
AS
A
Association
(p v (q v r)) :: ((p v q) v r)
(p • (q • r)) :: ((p • q) • r)
12
Q
DeM
A
DeMorgan’s Laws
~(p • q) :: (~p v ~q)
~(p v q) :: (~p • ~q)
13
Q
Cont
A
Contraposition
p —> q) :: (~p —> ~q
