This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# Conjunction

 gives the conjunction of expr over all choices of the Boolean variables .
• Conjunction effectively applies And to the results of substituting all possible combinations of True and False for the in expr.
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:
 Out[1]=

Show that a formula is a tautology:
 Out[1]=

Find the conditions on a for to be true for any b:
 Out[1]=
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