Conjunction (original) (raw)

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A product of ANDs, denoted

^ _(k=1)^nA_k.

The conjunctions of a Boolean algebra A of subsets of cardinality p are the 2^p functions

A_lambda= union _(i in lambda)A_i,

where lambda subset {1,2,...,p}. For example, the 8 conjunctions of A={A_1,A_2,A_3} are emptyset, A_1, A_2,A_3, A_1A_2, A_2A_3, A_3A_1, and A_1A_2A_3 (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 a_i.

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.

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Conjunction

Cite this as:

Weisstein, Eric W. "Conjunction." FromMathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Conjunction.html

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