Conjunction

Conjunction[expr,{a1,a2,}]

gives the conjunction of expr over all choices of the Boolean variables ai.

Details

Examples

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Basic Examples  (3)

The conjunction over a set of variables:

Show that a formula is a tautology:

Find the conditions on a for ab to be true for any b:

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:

Introduced in 2008
 (7.0)