Mathematica 9 is now available
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.
Wolfram Mathematica Documentation Center
DOCUMENTATION CENTER SEARCH
New to Mathematica? Find your learning path »
Mathematica > Mathematics and Algorithms > Discrete Mathematics > Boolean Computation > Conjunction >
Mathematica > Mathematics and Algorithms > Logic & Boolean Algebra > Boolean Computation > Conjunction >
Mathematica > Mathematics and Algorithms > Graphs & Networks > Graph Programming > Boolean Computation > Conjunction >
BUILT-IN MATHEMATICA SYMBOLSee Also »|More About »

Conjunction


gives the conjunction of expr over all choices of the Boolean variables .
MORE INFORMATION
  • Conjunction effectively applies And to the results of substituting all possible combinations of True and False for the in expr.
EXAMPLESCLOSE ALL
Basic Examples   (3)
The conjunction over a set of variables:
Show that a formula is a tautology:
Find the conditions on a for to be true for any b:
The conjunction over a set of variables:
In[1]:=
Click for copyable input
Out[1]=
 
Show that a formula is a tautology:
In[1]:=
Click for copyable input
Out[1]=
 
Find the conditions on a for to be true for any b:
In[1]:=
Click for copyable input
Out[1]=
Properties & Relations   (5)
Conjunction effectively computes the And over all truth values of the listed variables:
Conjunction is typically more efficient and can handle large numbers of variables:
Conjunction effectively eliminates (ForAll) quantifiers for the list of variables:
Use Resolve to eliminate more general combinations of quantifiers:
TautologyQ is Conjunction over all variables:
Use Disjunction to compute Or over a list of variables:
Disjunction is related to Conjunction by de Morgan's law:
Conjunction is repeated And, just as Product is repeated Times:
Represent Conjunction in terms of Product:
New in 7
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team
Format:   HTML  |  CDF