Conjunction
المؤلف:
Comtet, L.
المصدر:
Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. Dordrecht, Netherlands: Reidel
الجزء والصفحة:
...
11-1-2022
1038
Conjunction
A product of ANDs, denoted
The conjunctions of a Boolean algebra 
of subsets of cardinality 
are the 
functions
where ![lambda subset <span style=]()
{1,2,...,p}" src="https://mathworld.wolfram.com/images/equations/Conjunction/Inline4.gif" style="height:16px; width:90px" />. For example, the 8 conjunctions of ![A=<span style=]()
{A_1,A_2,A_3}" src="https://mathworld.wolfram.com/images/equations/Conjunction/Inline5.gif" style="height:16px; width:94px" /> are 
, 
, 
, 
, 
, 
, 
, and 
(Comtet 1974, p. 186).
A literal is considered a (degenerate) conjunction (Mendelson 1997, p. 30).
The Wolfram Language command Conjunction[expr, ![<span style=]()
{" src="https://mathworld.wolfram.com/images/equations/Conjunction/Inline14.gif" style="height:16px; width:4px" />a1, a2, ...![<span style=]()
}" src="https://mathworld.wolfram.com/images/equations/Conjunction/Inline15.gif" style="height:16px; width:4px" />] gives the conjunction of expr over all choices of the Boolean variables 
.
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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