Logical Equivalences Theorems Flashcards
1
Q
p ^ q ≡ q ^ p
p v q ≡ q v p
A
Commutative laws
2
Q
(p ^ q) ^ r ≡ p ^ (q ^ r)
(p v q) v r ≡ p v (q v r)
A
Associative Laws
3
Q
p ^ (q v r) ≡ (p ^ q) v (p ^ r)
p v (q ^ r) ≡ (p v q) ^ (p v r)
A
Distributive Laws
4
Q
(p v q) ^ (p v ~q) ≡ p v (q ^ ~q)
(p ^ q) v (p ^ ~q) ≡ p ^ (q v ~q)
A
Distributive Laws
5
Q
p ^ t ≡ p
p v c ≡ p
A
Identity Laws
6
Q
p v ~p ≡ t
p ^ ~p ≡ c
A
Negation Laws
7
Q
~(~p) ≡ p
A
Double Negative Law
8
Q
p ^ p ≡ p
p v p ≡ p
A
Idempotent Laws
9
Q
p v t ≡ t
p ^ c ≡ c
A
Universal bound Laws
10
Q
~(p ^ q) ≡ ~p v ~q
~(p v q) ≡ ~p ^ ~q
A
De Morgan’s Laws
11
Q
p v (p ^ q) ≡ p
p ^ (p v q) ≡ p
A
Absorption laws
12
Q
~t ≡ c
~c ≡ t
A
Negations of t and c
