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Or

See Also
- Xor
- BooleanConvert
- LogicalExpand
- BitOr
- Nor
- And
- Not
- Disjunction
- Union
- BooleanCountingFunction
- AnyTrue
- Characters
- \[Or]
Related Guides
Tech Notes
- Relational and Logical Operators
- Solving Logical Combinations of Equations

Or

e₁||e₂||…

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.

Details

Or[e₁,e₂,…] can be input in StandardForm and InputForm as . The character can be entered as ||, or, 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 are 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 or:

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 a Wolfram Language program:

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≥0 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 (7)

Truth table for binary Or:

Ternary Or:

Zero-argument Or is False:

Or with a single argument will return the evaluated argument regardless of value:

&& 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:

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