A product of ANDs, denoted
The conjunctions of a Boolean algebra of subsets of cardinality are the functions
where .
For example, the 8 conjunctions of are , , ,
, , , , and (Comtet 1974, p. 186).
A literal is considered a (degenerate) conjunction (Mendelson
1997, p. 30).
The Wolfram Language command Conjunction[expr,
a1, a2, ...] gives the conjunction of expr over all choices of
the Boolean variables .
See also
AND,
Boolean Algebra,
Boolean Function,
Complete
Product,
Disjunction,
NOT,
OR
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References
Comtet, L. Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. Dordrecht,
Netherlands: Reidel, p. 186, 1974.Mendelson, E. Introduction
to Mathematical Logic, 4th ed. London: Chapman & Hall, 1997.
Cite this as:
Weisstein, Eric W. "Conjunction." From
MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Conjunction.html
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