# Disjunction

Disjunction[expr,{a1,a2,}]

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

# Details • Disjunction[expr,{a1,a2,}] applies Or to the results of substituting all possible combinations of True and False for the ai in expr.
• Disjunction gives a resolved form of .
• Disjunction is to Or what Sum is to Plus.

# Examples

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## Basic Examples(3)

The disjunction over a set of variables:

Check whether an expression is satisfiable:

Find the conditions on a for ab to be satisfiable:

## Properties & Relations(5)

Disjunction effectively computes the Or over all truth values of the listed variables:

Disjunction is typically more efficient and can work large numbers of variables:

Disjunction eliminates (Exists) quantifiers for the list of variables:

Use Resolve to eliminate more general combinations of quantifiers:

SatisfiableQ is Disjunction over all variables:

Use Conjunction to compute And over a list of variables:

Conjunction is related to Disjunction by de Morgan's law:

Disjunction is effectively repeated Or, just as Sum is repeated Plus:

Represent Disjunction in terms of Sum: