5.9: Chapter Review

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 both $p$ and $q$ are true or both are 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.