Logic - Equivalences Flashcards
(19 cards)
1
Q
A ∧ B
A
B ∧ A
Commutativity of ∧
2
Q
A ∧ A
A
A
Idempotence of ∧
3
Q
A ∧ T
T ∧ A
A
A
4
Q
⊥ ∧ A
A ∧ ⊥
A ∧ ¬A
¬A ∧ A
A
⊥
5
Q
(A ∧ B) ∧ C
A
A ∧ (B ∧ C)
6
Q
A ∨ B
A
B ∨ A
Commutativity of ∨
7
Q
A ∨ A
A
A
Idempotence of ∨
8
Q
T ∨ A
A ∨ T
A ∨ ¬A
¬A ∨ A
A
T
9
Q
A ∨ ⊥
⊥ ∨ A
A
A
10
Q
(A ∨ B) ∨ C
A
A ∨ (B ∨ C)
11
Q
A → A
A
T
12
Q
T → A
A
A
13
Q
A → T
A
T
14
Q
⊥ → A
A
T
15
Q
A → ⊥
A
¬A
16
Q
A → B
A
¬A ∨ B
17
Q
A ↔ B
A
(A → B) ∧ (B → A)
(A ∧ B) ∨ (¬A ∧ ¬B)
¬A ↔ ¬B
18
Q
A ∧ (B ∨ C)
A
(A ∧ B) ∨ (A ∧ C).
Distributivity of ∨, ∧
19
Q
A ∧ (A ∨ B)
A
A ∨ (A ∧ B)
