Logical Equivalence Flashcards
1
Q
Identity Law 1
A
p ∧ T ≡ p
2
Q
Identity Law 2
A
p ∨ F ≡ p
3
Q
Domination Law 1
A
p ∨ T ≡ T
4
Q
Domination Law 2
A
p ∧ F ≡ F
5
Q
Idempotent Law 1
A
p ∨ p ≡ p
6
Q
Idempotent Law 2
A
p ∧ p ≡ p
7
Q
Double Negation Law
A
¬(¬p) ≡ p
8
Q
Negation Law 1
A
p ∨ ¬p ≡ T
9
Q
Negation Law 2
A
p ∧ ¬p ≡ F
10
Q
Commutative Law 1
A
p ∨ q ≡ q ∨ p
11
Q
Commutative Law 2
A
p ∧ q ≡ q ∧ p
12
Q
Associative Law 1
A
(p ∨ q) ∨ r ≡ p ∨ (q ∨ r)
13
Q
Associative Law 2
A
(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)
14
Q
Distributive Law 1
A
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
15
Q
Distributive Law 2
A
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
16
Q
Absorption Law 1
A
p ∨ (p ∧ q) ≡ p
17
Q
Absorption Law 2
A
p ∧ (p ∨ q) ≡ p
18
Q
De Morgan’s Law 1
A
¬(p ∧ q) ≡ ¬p ∨ ¬q
19
Q
De Morgan’s Law 2
A
¬(p ∨ q) ≡ ¬p ∧ ¬q
20
Q
Conditional 1
A
p → q ≡ ¬p ∨ q
21
Q
Conditional 2
A
p → q ≡ ¬q → ¬p
22
Q
Conditional 3
A
p ∨ q ≡ ¬p → q
23
Q
Conditional 4
A
p ∧ q ≡ ¬(p → ¬q)
24
Q
Conditional 5
A
¬(p → q) ≡ p ∧ ¬q
25
Conditional 6
(p → q) ∧ (p → r) ≡ p → (q ∧ r)
26
Conditional 7
(p → r) ∧ (q → r) ≡ (p ∨ q) → r
27
Conditional 8
(p → q) ∨ (p → r) ≡ p → (q ∨ r)
28
Conditional 9
(p → r) ∨ (q → r) ≡ (p ∧ q) → r
29
Biconditional 1
p ↔ q ≡ (p → q) ∧ (q → p)
30
Biconditional 2
p ↔ q ≡ ¬p ↔ ¬q
31
Biconditional 3
p ↔ q ≡ (p ∧ q) ∨ (¬p ∧ ¬q)
32
Biconditional 4
¬(p ↔ q) ≡ p ↔ ¬q
