Logic: Negations, Disjunctions, Conjunctions, and Truth Tables

Vocabulary flashcards covering the definitions, symbols, truth conditions, and truth tables for logical negations, disjunctions, and conjunctions.

Negation ($\sim$)

A logical operation symbolized by $\sim$ that makes a true statement false and makes a false statement true.

Disjunction ($\lor$)

A compound statement using "OR" (symbolized by $\lor$ or $U$) that is only true when at least one part of the statement is true.

Conjunction ($\land$)

A compound statement using "AND" (symbolized by $\land$ or $\cap$) that is only true when both parts of the statement are true.

Negation of a Statement

The logical reversal of the truth value of a statement; for example, if $P$ ("There are $4$ quarters in a dollar") is true, then $\sim P$ ("There are not $4$ quarters in a dollar") is false.

Truth Condition for Disjunction

An "OR" statement evaluates to true if at least one component statement is true; it evaluates to false only when both component statements are false (such as when both components are negated to false).

Truth Condition for Conjunction

An "AND" statement evaluates to true strictly when both component statements are true; it evaluates to false if one or both component statements are false.

Truth Table for $\sim p \lor \sim q$

A truth table evaluating $\sim p \lor \sim q$, which outputs False when $p$ is True and $q$ is True, and outputs True for all other combinations: $(T, F)$, $(F, T)$, and $(F, F)$.

Truth Table for $\sim p \land \sim q$

A truth table evaluating $\sim p \land \sim q$, which outputs True only when both $p$ and $q$ are False, and outputs False for all other combinations: $(T, T)$, $(T, F)$, and $(F, T)$.