<*logic*>
The dyadic truth function "not both". One of only
two dyadic truth
functions capable of expressing all truth functions
by itself.
Notation:
p|q. Also called the Sheffer stroke, and alternative
denial.
See dagger function

[Glossary of First-Order Logic]

p q p | q T T F T F T F T T F F TA truth-functional connective that suffices to symbolize every dyadic relation between statements. Since " p | q " (or "not both p and q") takes the truth-values illustrated in the {truth-table} at right, negation can be defined as " p | p " and disjunction as " ( p | p ) | ( q | q )". From these, in turn, all of the other connectives can be derived. Recommended Reading: Willard V. O. Quine, Mathematical Logic (Harvard, 1981) and Alfred North Whitehead and Bertrand Arthur Russell, Principia Mathematica to 56 (Cambridge, 1997).

[A Dictionary of Philosophical Terms and Names]

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