Cheatography

# Logic Cheat Sheet by mariusvnh

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.