Or
Details
- Or [e1,e2,…] can be input in StandardForm and InputForm as e_(1)∨e_(2)∨.... The character ∨ can be entered as ||, or, or \[Or] .
- Or has attribute HoldAll , and explicitly controls the evaluation of its arguments. In e_(1)||e_(2)||... the e_(i) 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
open all close allBasic 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 :
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:
See Also
Xor BooleanConvert LogicalExpand BitOr Nor And Not Disjunction Union BooleanCountingFunction AnyTrue
Characters: \[Or]
Function Repository: VennDiagram
Related Guides
History
Introduced in 1988 (1.0) | Updated in 1996 (3.0)
Text
Wolfram Research (1988), Or, Wolfram Language function, https://reference.wolfram.com/language/ref/Or.html (updated 1996).
CMS
Wolfram Language. 1988. "Or." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/Or.html.
APA
Wolfram Language. (1988). Or. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Or.html
BibTeX
@misc{reference.wolfram_2025_or, author="Wolfram Research", title="{Or}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/Or.html}", note=[Accessed: 06-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_or, organization={Wolfram Research}, title={Or}, year={1996}, url={https://reference.wolfram.com/language/ref/Or.html}, note=[Accessed: 06-January-2026]}