Definition:Logical Connective/Binary

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.

There is a total of 16 possible binary connectives, a subset of which is usually used in the pursual of symbolic logic:


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


 * Disjunction: the "Or" connective $$p \or q$$: "$$p$$ 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 $$q$$."