Definition:Logical Connective/Binary

Definition
A binary logical connective (or two-place connective) is a connective whose effect on its compound statement is determined by the truth value of two substatements.

In standard Aristotelian logic, there are 16 binary logical connectives, cf. Binary Boolean Functions.

In the field of symbolic logic, the following four (symbols for) binary logical connectives are commonly used:


 * Conjunction: the And connective $p \land q$: $p$ is true and $q$ is true.


 * Disjunction: the Or connective $p \lor q$: $p$ is true or $q$ is true, or possibly both.


 * The conditional connective $p \implies q$: If $p$ is true, then $q$ is true.


 * The material equivalence connective $p \iff q$: $p$ is true if and only if $q$ is true, or $p$ is equivalent to $q$.