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Disjunction

Disjunction[expr, {a1, a2, ...}]
gives the disjunction of expr over all choices of the Boolean variables ai.
  • Disjunction[expr, {a1, a2, ...}] applies Or to the results of substituting all possible combinations of True and False for the ai in expr.
EXAMPLESCLOSE ALL
Basic Examples   (3)
The disjunction over a set of variables:
Check whether an expression is satisfiable:
Find the conditions on a for aNorb to be satisfiable:
The disjunction over a set of variables:
In[1]:=
Click for copyable input
Out[1]=
 
Check whether an expression is satisfiable:
In[1]:=
Click for copyable input
Out[1]=
 
Find the conditions on a for aNorb to be satisfiable:
In[1]:=
Click for copyable input
Out[1]=
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 (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:
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