Quiz 5 - transformations and whatever Flashcards
1
Q
Modus ponens
A
p ⊃ q
p /: q
2
Q
Conjunction
A
p
q/: p * q
3
Q
Modus Tollens
A
p ⊃ q
~q /: ~p
4
Q
Hypothetical syllogism
A
p ⊃ q
q ⊃ r /: p ⊃ r
5
Q
Disjunctive syllogism
A
p v q
~ p /: q
p v q
~q /:p
6
Q
Addition
A
p /: p v q
7
Q
Constructive Dilemma
A
p v q
p ⊃ r
q ⊃ s /: r v s
8
Q
Simplification
A
p * q /: p
p * q /: q
9
Q
Double negation
A
p :: ~~ p
10
Q
Contraposition
A
(p ⊃ q) :: (~q ⊃ ~p)
11
Q
DeMorgan’s Theorem
A
~(p * q):: (~p v ~q)
~(p v q):: (~p * ~q)
12
Q
Implication
A
(p ⊃ q):: (~p v q)
13
Q
Commutation
A
(p v q) :: (q v p)
p * q):: (q* p
14
Q
Exportation
A
[(p * q) ⊃ r] :: [p ⊃ (q ⊃ r)]
15
Q
Association
A
[p v (q v r)] :: [(p v q) v r]
[p * ( q * r)] :: [(p * q) * r]
16
Q
Tautology
A
p :: ( p * p)
p :: (p v p)
17
Q
Distribution
A
[p * (q v r)] :: [(p * q) v (p * r)]
[p v (q * r)] :: [(p v q) * (p v r)]
18
Q
Equivalence
A
(p = q) :: [(p ⊃ q) * (q ⊃ p)]
(p = q) :: [(p * q) v (~p * ~q)]
