Complete Product
المؤلف:
Comtet, L
المصدر:
Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. Dordrecht, Netherlands: Reidel
الجزء والصفحة:
p. 186
11-1-2022
1172
Complete Product
The complete products of a Boolean algebra of subsets generated by a set ![<span style=]()
{A_k}_(k=1)^p" src="https://mathworld.wolfram.com/images/equations/CompleteProduct/Inline1.gif" style="height:19px; width:41px" /> of cardinal number 
are the 
Boolean functions
 |
(1)
|
where each 
may equal 
or its complement 
. For example, the 
complete products of ![A=<span style=]()
{A_1,A_2,A_3}" src="https://mathworld.wolfram.com/images/equations/CompleteProduct/Inline8.gif" style="height:16px; width:94px" /> are
 |
(2)
|
Each Boolean function has a unique representation (up to order) as a union of complete products. For example,
(Comtet 1974, p. 186).
REFERENCES:
Comtet, L. Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. Dordrecht, Netherlands: Reidel, p. 186, 1974.
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