Replacement Rules Flashcards
1
Q
example:
Р == (p v p)
Р == (p ^ p)
A
idempotence
2
Q
examples:
(p v q) == (q v p)
(p ^ q) == (q ^ p)
A
commutativity
3
Q
examples:
[p v (q v r)] == [(p v q) v r]
[(p ^ q) ^ r)] == [(p ^ q) ^ r]
A
associativity
4
Q
¬(p v q) == ¬p ^ ¬q
¬(p ^ q) == ¬p v ¬q
A
De Morgan’s Law
5
Q
[p v (q ^ r)] == (p v q) ^ (p v r)];
A
distributivity of v over ^
6
Q
[p ^ (q v r)] == (p ^ q) v (p ^ r)];
A
distributivity of ^ over v
7
Q
P == ¬(¬P)
A
double negation
8
Q
(p -> q) == (¬p v q)
A
Material Implication
9
Q
(p q) == [(p –> q) ^ (q –> p)
A
material equivalence
10
Q
[(p –> q) ^ (p –> ¬q)] == ¬p
A
absurdity
11
Q
p –> q == ¬q –> ¬p
A
contrapositive or transposition
12
Q
p ^ ¬p == c
p v ¬p == t
A
negation laws
13
Q
p ^ c == c
p v t == t
A
universal bound laws
14
Q
p ^ t == p
p v c == p
A
identity laws
15
Q
p v (p ^ q) == p p ^ (p v q) == p
A
absorption laws
