Logical Connectors and Truth Tables

Vocabulary practice cards focusing on logical connectives (conjunction, disjunction, conditional, and biconditional), their notations, readings, and truth table values.

Conjunction ($\wedge$)

A logical connector that joins two propositions using the word "and" ("y"), denoted as $p \wedge q$ and read as "$p$ and $q$".

Truth conditions of a Conjunction ($p \wedge q$)

A proposition that is true ($\text{V}$) only when both propositions $p$ and $q$ are true; it is false ($\text{F}$) if either or both propositions are false.

Disjunction ($\vee$)

A logical connector that joins two propositions using the word "or" ("o"), denoted as $p \vee q$ and read as "$p$ or $q$".

Truth conditions of a Disjunction ($p \vee q$)

A proposition that is true ($\text{V}$) if at least one of the component propositions is true, and false ($\text{F}$) only when both $p$ and $q$ are false.

Conditional ($\rightarrow$)

A logical connector expressing cause and consequence, where the first proposition is an indispensable requirement for the second to be fulfilled; written as $p \rightarrow q$ and read as "If $p$, then $q$".

Truth conditions of a Conditional ($p \rightarrow q$)

A proposition that is false ($\text{F}$) only when the antecedent $p$ is true and the consequent $q$ is false; in all other cases (including when $p$ is false), it is true ($\text{V}$).

Biconditional ($\leftrightarrow$)

A logical connector expressing an equivalence relation between two propositions, holding only if both happen together; written as $p \leftrightarrow q$ and read as "$p$ if and only if $q$".

Truth conditions of a Biconditional ($p \leftrightarrow q$)

A proposition that is true ($\text{V}$) when both propositions share the same truth value (both true or both false), and false ($\text{F}$) when they have differing truth values.