5.8: Chapter Review and Glossary
- Page ID
- 113164
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Summary:
| Operation | Notation | Summary of truth values |
| Negation | \(\sim p\) | The opposite truth value of \(p\) |
| Conjunction |
\(p \wedge q\) |
True only when both \(p\) and \(q\) are true |
| Disjunction | \(p \vee q\) | False only when both \(p\) and \(q\) are false |
| Conditional |
\(p \to q\) |
False only when \(p\) is true and \(q\) is false |
| Biconditional |
\(p\leftrightarrow q\) |
True only when \(p\) and \(q\) are both true or \(p\) and \(q\) are both false |
Notations & Definitions:
- Negation: \(\sim\) or "not"
- Conjunction: \(\wedge\) or "and"
- Disjunction: \(\vee\) or "or"
- Conditional: \(\to\) or "implies" or "if/then"
- Biconditional: \(\leftrightarrow\) or "if and only if" or "iff"
- Counter-example: An example that disproves a mathematical proposition or statement.
- Logically Equivalent: \(\equiv\) Two propositions that have the same truth table result.
- Tautology: A statement that is always true, and a truth table yields only true results.
- Contradiction: A statement which is always false, and a truth table yields only false results.