Mathematics/Discrete Math/Propositional Logic
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Base Logic Symbols
| Symbol | → | ↔ | ¬ | ∧ | ∨ | ⊕ | ⊤ | ⊥ |
|---|---|---|---|---|---|---|---|---|
| Name | Material Implication | Material Equivalence | Negation | Logical Conjunction | Logical (Inclusive) Disjunction | Logical (Exclusive) Disjunction | Tautology | Contradiction |
| Definition | If...Then, | If and Only if (iff) | Not | True if all are True | True if one or more are True | True if exactly one is True | Unconditionally True | Unconditionally False |
| Notation Example | A → B | A ↔ B | ¬A | A ∧ B | A ∨ B | A ⊕ B | ⊤ A | ⊥ A |
| Verbal Explanation | If A is True, then B is also True. | A is True iff B is true. | A is not True. | True if both A and B are True. | True if at least one of A or B are True. | True if A or B is True, but not both. | A is always True | A is always False |
| Alternative Symbol | ⊃ | ≡ | ! / Ā | & | || | ⊻ |