BUILT-IN MATHEMATICA SYMBOL

Or

is the logical OR function. It evaluates its arguments in order, giving True immediately if any of them are True, and False if they are all False.

MORE INFORMATION

Or can be input in StandardForm and InputForm as . The character can be entered as Esc || Esc, Esc or Esc, or \[Or].

Or has attribute HoldAll, and explicitly controls the evaluation of its arguments. In the are evaluated in order, stopping if any of them is found to be True.

Or gives symbolic results when necessary, removing initial arguments that are False.

EXAMPLES

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Basic Examples (4)

Combine assertions with ||:

A symbolic disjunction:

A system of equations:

Enter using Esc or Esc:

Combine assertions with ||:

In[1]:=

Out[1]=

A symbolic disjunction:

In[1]:=

Out[1]=

A system of equations:

In[1]:=

Out[1]=

Enter using Esc or Esc:

In[1]:=

Out[1]=

Scope (5)

Or works with any number of arguments:

Or is associative:

Or with explicit True or False arguments will simplify:

Or evaluates its arguments in order, stopping when an argument evaluates to True:

The order of arguments may be important:

Symbolic transformations will not preserve argument ordering:

TraditionalForm formatting:

Applications (6)

Combine conditions in Mathematica code:

If an argument of Or evaluates to True, any subsequent arguments are not evaluated:

The argument order in Or matters; if the last two arguments are reversed, I

is evaluated:

Combine assumptions:

Combine equations and inequalities; Or is used both in the input and the output:

Use

to combine conditions:

A cellular automaton based on Or:

Find the area of the union of sets given by algebraic conditions:

This shows the set:

Properties & Relations (5)

Truth table for Or:

has higher precedence than

:

Use BooleanConvert to expand And with respect to Or:

De Morgan's laws relate And, Or, and Not:

Disjunction of conditions corresponds to the Max of Boole functions: