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BooleanVariables
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BooleanVariables

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gives a list of the Boolean variables in the Boolean expression expr.

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gives the number of Boolean variables in the BooleanFunction object bf.

Details

Examples

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Basic Examples  (2)Summary of the most common use cases

Find the variables in a Boolean expression:

In[1]:=1
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https://wolfram.com/xid/0dc2rklrib3a-ciabkx
Out[1]=1

Find the number of variables for a pure BooleanFunction object:

In[1]:=1
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https://wolfram.com/xid/0dc2rklrib3a-fg9s20
Out[1]=1

Scope  (2)Survey of the scope of standard use cases

Find the Boolean variables in a Boolean expression:

In[1]:=1
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https://wolfram.com/xid/0dc2rklrib3a-b9mba3
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dc2rklrib3a-kw1xoy
Out[2]=2

Programmatically get the number of arguments to a pure Boolean function:

In[1]:=1
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https://wolfram.com/xid/0dc2rklrib3a-cv9270
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dc2rklrib3a-c4lpjh
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0dc2rklrib3a-82k2r
Out[3]=3

Properties & Relations  (2)Properties of the function, and connections to other functions

BooleanVariables is by default used as the list of variables for BooleanTable:

In[1]:=1
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https://wolfram.com/xid/0dc2rklrib3a-gnytmw
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dc2rklrib3a-fpxlt2
Out[2]=2

Use BooleanVariables to get a variable list for SatisfiabilityInstances:

In[1]:=1
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https://wolfram.com/xid/0dc2rklrib3a-je6zz0
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0dc2rklrib3a-c6t8x8
Out[2]=2

FindInstance:

In[3]:=3
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https://wolfram.com/xid/0dc2rklrib3a-etstd1
Out[3]=3

Conjunction and Disjunction:

In[4]:=4
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https://wolfram.com/xid/0dc2rklrib3a-d3ocww
Out[4]=4
In[5]:=5
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https://wolfram.com/xid/0dc2rklrib3a-14fhi
Out[5]=5

Possible Issues  (1)Common pitfalls and unexpected behavior

Anything that is not explicitly constructed using Boolean primitives and functions is variable:

In[1]:=1
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https://wolfram.com/xid/0dc2rklrib3a-dtw9hg
Out[1]=1
Wolfram Research (2008), BooleanVariables, Wolfram Language function, https://reference.wolfram.com/language/ref/BooleanVariables.html.
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Wolfram Research (2008), BooleanVariables, Wolfram Language function, https://reference.wolfram.com/language/ref/BooleanVariables.html.

Text

Wolfram Research (2008), BooleanVariables, Wolfram Language function, https://reference.wolfram.com/language/ref/BooleanVariables.html.

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Wolfram Research (2008), BooleanVariables, Wolfram Language function, https://reference.wolfram.com/language/ref/BooleanVariables.html.

CMS

Wolfram Language. 2008. "BooleanVariables." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BooleanVariables.html.

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Wolfram Language. 2008. "BooleanVariables." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BooleanVariables.html.

APA

Wolfram Language. (2008). BooleanVariables. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BooleanVariables.html

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Wolfram Language. (2008). BooleanVariables. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BooleanVariables.html

BibTeX

@misc{reference.wolfram_2025_booleanvariables, author="Wolfram Research", title="{BooleanVariables}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/BooleanVariables.html}", note=[Accessed: 08-July-2025 ]}

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@misc{reference.wolfram_2025_booleanvariables, author="Wolfram Research", title="{BooleanVariables}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/BooleanVariables.html}", note=[Accessed: 08-July-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_booleanvariables, organization={Wolfram Research}, title={BooleanVariables}, year={2008}, url={https://reference.wolfram.com/language/ref/BooleanVariables.html}, note=[Accessed: 08-July-2025 ]}

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@online{reference.wolfram_2025_booleanvariables, organization={Wolfram Research}, title={BooleanVariables}, year={2008}, url={https://reference.wolfram.com/language/ref/BooleanVariables.html}, note=[Accessed: 08-July-2025 ]}