Logical Equivalences Flashcards
1
Q
Domination Laws
A
P ∨ T = T
P ∧ F = F
2
Q
Idempotent Laws
A
P ∨ P = P
P ∧ P = P
3
Q
Double Negation Law
A
¬(¬P) = P
4
Q
Commutative Law
A
P ∨ Q = Q ∨ P
P ∧ Q = Q ∧ P
5
Q
Associative Law
A
(P ∨ Q) ∨ R = P ∨ (Q ∨ R)
P ∧ Q) ∧ R = P ∧ (Q ∧ R
6
Q
Distributive Law
A
P ∨ (Q ∧ R) = (P ∨ Q) ∧ (P ∨ R)
P ∧ (Q ∨ R) = (P ∧ Q) ∨ (P ∧ R)
7
Q
DeMorgan’s Laws
A
¬(P ∧ Q) = ¬P ∨ ¬Q
¬(P ∨ Q) = ¬P ∧ ¬Q
8
Q
Absorption Laws
A
P ∨ (P ∧ Q) = P
P ∧ (P ∨ Q) = P
9
Q
Negation Law
A
P ∨ ¬P = T
P ∧ ¬P = F
10
Q
Identity Laws
A
P ∨ F = P
P ∧ T = P
11
Q
Universal Instantiation
A
∀xP(x)
∴P(c)
12
Q
Universal Generalization
A
P(c) for arbitrary c
∴∀xP(x)
13
Q
Existential Instantiation
A
∃xP(x)
∴P(c) for some element c
14
Q
Existential Generalization
A
P(c) for some element c
∴∃xP(x)
15
Q
Universal Modus Ponens
A
∀x(P(x)→Q(x))
P(a), where a is particular element in the domain
∴Q(a)
