Cheatography
https://cheatography.com
A simple cheat sheet that describes logical operator and their use
Logical Operators
Not |
Negation |
NOT |
¬ |
And |
Conjunction |
AND |
∧ |
Or |
Disjunction |
OR |
∨ |
Exclusive Or |
N/A |
XOR |
⊕ |
N/A |
Implication |
IMPLIES |
→ |
Equal |
Equivalence |
EQUAL |
↔ |
Precedence
NOT |
AND, NAND |
OR, NOR |
IMPLIES |
EQUAL, XOR |
|
|
Commutativity
A op B == B op A
Works for AND, OR, EQUAL, XOR, NAND, and NOR |
The only operator that isn't commutative is IMPLIES
Associativity
A op (B op C) == (A op B) op C
Works for AND, OR, EQUAL, and XOR. |
Distributivity
A ∨ (B ∧ C) |
== |
(A ∨ B) ∧ (A ∨ C) |
A ∧ (B ∨ C) |
== |
(A ∧ B) ∨ (A ∧ C) |
Implies Truth Table
A |
B |
Result |
False |
False |
True |
True |
False |
False |
False |
True |
True |
True |
True |
True |
|
|
Equivalents Formulae
A ↔ B |
== |
(A → B) ∧ (B → A) |
A ⊕ B |
== |
¬(A → B) ∨ ¬(B → A) |
A → B |
== |
¬A ∨ B |
A → B |
== |
¬(A ∧ ¬B) |
A ∨ B |
== |
¬(¬A ∧ ¬B) |
A ∨ B |
== |
¬A → B |
A ∧ B |
== |
¬(¬A ∨ ¬B) |
A ∧ B |
== |
¬(A → ¬B) |
Sementic Tableaux
If you are asked to prove something with sementic tableaux, negate the formulae first.
If you are asked to refute something with the sementic tableaux, do not negate the formulae. |
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