Logical connectives are the symbols and words that build new statements from old ones. In this unit, we study negation, conjunction, inclusive disjunction, exclusive disjunction, implication, and biconditional. The focus keyword logical connectives appears throughout this page because these connectives are the working tools of mathematical logic. Once you know the meaning of each connective, a long sentence can be read as a carefully built logical expression instead of as a confusing piece of English.

A logical connective is a word or symbol used to form a compound statement from one or more statements. The truth value of the compound statement is determined by the truth values of its component statements and the connective used. Example from arithmetic: if $p$ means "$2$ is even" and $q$ means "$3$ is odd", then $p\land q$ means "$2$ is even and $3$ is odd." Example from geometry: if $r$ means "Every square is a rectangle", then $\neg r$ means "It is not true that every square is a rectangle." Example from daily language: if $s$ means "It is raining" and $t$ means "The ground is wet", then $s\rightarrow t$ means "If it is raining, then the ground is wet."