logical connective

#LaTeX

A logical connective is an operator in an operation that combines or modifies one or more logical variables or formulas (propositions) for the purposes of propositional logic.

English word	Connective	Symbol	$L A T E X$	Logical Gate
not	negation	$\neg$	`\neg`	NOT gate
and	conjunction	$\land$	`\wedge`	AND gate
not both	alternative denial	$↑$	`\uparrow`	NAND gate
or	disjunction	$\lor$	`\vee`	OR gate
neither...nor	joint denial	$↓$	`\downarrow`	NOR gate
if...then	material implication	$\Rightarrow$	`\Rightarrow`
but not	material nonimplication	$⇏$	`\nRightarrow`
...if	converse implication	$\Leftarrow$	`\Leftarrow`
not...but	converse nonimplication	$⇍$	`\nLeftarrow`
if and only if	biconditional	$\Leftrightarrow$	`\Leftrightarrow`	XNOR gate
either...or	exclusive disjunction	$↮$	`\nleftrightarrow`	XOR gate

For a binary operation which is a truth function, given two operands which have binary truth value, there are $2^{2} = 4$ possible input combinations, so there are $2^{4} = 16$ possible truth tables for truth functions. Therefore, any truth function can be shown to be equivalent to one of these 16 forms. Each is classified as follows:

either proposition as itself,
negation of either proposition,
conjunction, alternative denial,
disjunction, joint denial,
material implication, material nonimplication,
converse implication, converse nonimplication,
biconditional, exclusive disjunction,
tautology, contradiction,