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