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
Explore with Wolfram|Alpha
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
Subject classifications
