Properties of Operations on Statements (Logical Operations)
What are Statements? In mathematical logic, a statement (or proposition) is a declarative sentence that is either TRUE (T) or FALSE (F), but not both. We perform operations on statements using logical connectives.
📌 Basic Logical Operations
| Operation | Symbol | Name | Meaning |
|---|---|---|---|
| Negation | $ \sim p $ or $ \neg p $ | NOT | Opposite truth value of $p$ |
| Conjunction | $ p \wedge q $ | AND | True only when BOTH are true |
| Disjunction | $ p \vee q $ | OR | True when AT LEAST ONE is true |
| Conditional | $ p \rightarrow q $ | IF...THEN | False only when $p$ is true and $q$ is false |
| Biconditional | $ p \leftrightarrow q $ | IF AND ONLY IF | True when both have SAME truth value |