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Connective

A function, or the symbol representing a function, which corresponds to English conjunctions such as "and," "or," "not," etc. that takes one or more truth values as input and returns a single truth value as output. The terms "logical connective" and "propositional connective" (Mendelson 1997, p. 13) are also used. The following table summarizes some common connectives and their notations.

connectivesymbol
ANDA ^ B, A·B, A.B, AB, A&B, A&&B
equivalentA=B, A<=>B, A<->B
impliesA=>B, A superset B, A->B
NANDA nand B, A|B, A·B^_
nonequivalentA≢B, A<=>AdjustmentBox[/, BoxMargins -> {{-1.05, 0.13913}, {-0.5, 0.5}}]B, A<->AdjustmentBox[/, BoxMargins -> {{-1, 0.13913}, {-0.5, 0.5}}]B
NORA nor B, AvB, A+B^_
NOT!A, ¬A, A^_, ∼A
ORA v B, A+B, A|B, A∥B
XNORA XNOR B
XORA xor B, A direct sum B

See also

AND, Binary Operator, Equivalent, Implies, OR, NAND, Nonequivalent, NOR, NOT, Propositional Calculus, Statement Form, Truth Table, XNOR, XOR

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References

Mendelson, E. Introduction to Mathematical Logic, 4th ed. London: Chapman & Hall, 1997.

Referenced on Wolfram|Alpha

Connective

Cite this as:

Weisstein, Eric W. "Connective." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Connective.html

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