math-propositional-logic.html
* created: 2025-06-17T17:47
* modified: 2025-07-03T08:52
title
Propositional Logic
description
Represents some kind of statement that can either be true or false. There are a couple of propositional logic operators like $\land$ (and) or $\lor$ (or) which can be used to express such logic.
Description
Propositional logic is a formal system in logic that deals with propositions (also called statements) and logical connectives. A proposition is a statement that is either true or false, but not both.
| Symbol |
Definition |
| \lnot A |
NOT A — true if A is false |
| A \land B |
A AND B — true if both A and B are true |
| A \lor B |
A OR B — true if at least one of A or B is true |
| A \oplus B |
A XOR B — true if exactly one of A or B is true |
| A \Rightarrow B |
A → B — false only if A is true and B is false |
| A \Leftrightarrow B |
A ↔ B — true if A and B are both true or both false |
De Morgan's law
De Morgan’s laws express how negation interacts with logical conjunction ("and") and logical disjunction ("or").
- \neg (A \land B) \Leftrightarrow (\neg A) \lor (\neg B)
- \neg(A \lor B) \Leftrightarrow (\neg A) \land (\neg B)