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  "body": "\n## Definition\n\nLet $n \\ge 0$ be an integer, and write $\\mathsf{T}$ and $\\mathsf{F}$ for the two truth values.\nAn $n$-ary *logical connective* of classical [[propositional logic|09K9MWD2QQ]] is a symbol $c$ with a truth function $f_c \\colon \\set{\\mathsf{T}, \\mathsf{F}}^n \\to \\set{\\mathsf{T}, \\mathsf{F}}$.\nFor formulas $\\varphi_1, \\dots, \\varphi_n$, the expression $c(\\varphi_1, \\dots, \\varphi_n)$ is again a formula.\nUnder a truth assignment, its value is $f_c$ applied to the values of $\\varphi_1, \\dots, \\varphi_n$.\n\n## Remarks\n\nConjunction $\\land$ is a binary connective: $f_\\land(a, b) = \\mathsf{T}$ exactly when $a = b = \\mathsf{T}$.\nSo $p \\land q$ is true only when [[propositions|0ZGC7ZESYN]] $p$ and $q$ are both true.\nThe modal operator \"it is necessary that\" is not a connective of classical propositional logic.\nIt has no truth function: the truth of $p$ does not determine whether $p$ is necessary.\nBinary connectives are written in infix form, such as $\\varphi \\to \\psi$.\nThe set $\\set{\\neg, \\land}$ is functionally complete: every truth function is expressed by a formula built with these two.\nThe single connective NAND, with $f(a, b) = \\mathsf{F}$ exactly when $a = b = \\mathsf{T}$, is also functionally complete.\n",
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