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Conjunction

Conjunction[expr,{a_(1),a_(2),...}]
gives the conjunction of expr over all choices of the Boolean variables ai.
  • Conjunction[expr, {a1, a2, ...}] effectively applies And to the results of substituting all possible combinations of True and False for the ai 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 aImpliesb 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 aImpliesb 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 (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:
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