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Equivalent
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Equivalent

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Equivalent[e1,e2,…]

represents the logical equivalence e1⇔e2⇔…, giving True when all of the ei are the same.

Details

Examples

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

Test equivalence of Boolean expressions:

In[1]:=1
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https://wolfram.com/xid/09bsqslje-k6xm1v
Out[1]=1

Enter using equiv:

In[1]:=1
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https://wolfram.com/xid/09bsqslje-t0yea
Out[1]=1

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

Automatic simplifications:

In[1]:=1
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https://wolfram.com/xid/09bsqslje-d6xaj5
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09bsqslje-pii5d
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/09bsqslje-n1u3o
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/09bsqslje-f4r0kc
Out[4]=4

TraditionalForm formatting:

In[1]:=1
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https://wolfram.com/xid/09bsqslje-tlbau

Applications  (1)Sample problems that can be solved with this function

Prove equivalence between different Boolean expressions:

In[1]:=1
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https://wolfram.com/xid/09bsqslje-fm96al
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09bsqslje-jbic8y
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/09bsqslje-cmukwj
Out[3]=3

Properties & Relations  (7)Properties of the function, and connections to other functions

Truth table for binary Equivalent:

In[1]:=1
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https://wolfram.com/xid/09bsqslje-ib02ro
Out[1]=1

Ternary Equivalent:

In[2]:=2
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https://wolfram.com/xid/09bsqslje-cwl4xo
Out[2]=2

Use BooleanConvert to express Equivalent in terms of And and Or:

In[1]:=1
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https://wolfram.com/xid/09bsqslje-6wqta
Out[1]=1

A well-known representation of two-argument Equivalent in terms of Implies:

In[1]:=1
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https://wolfram.com/xid/09bsqslje-bnvdb4

This proves that the two representations are indeed equivalent:

In[2]:=2
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https://wolfram.com/xid/09bsqslje-ferwu5
Out[2]=2

Equivalent can be represented in terms of BooleanCountingFunction:

In[1]:=1
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https://wolfram.com/xid/09bsqslje-c8xadt
In[2]:=2
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https://wolfram.com/xid/09bsqslje-fiw5x
Out[2]=2

Equivalent with two arguments is equivalent to Xnor:

In[1]:=1
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https://wolfram.com/xid/09bsqslje-fnegrd
Out[1]=1

For more arguments, these are different primitives:

In[2]:=2
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https://wolfram.com/xid/09bsqslje-iss6ws
Out[2]=2

Use Resolve to prove equivalence of two systems of equations:

In[1]:=1
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https://wolfram.com/xid/09bsqslje-tbytp
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09bsqslje-jdnclu
Out[2]=2

Equivalent is effectively Equal for Boolean expressions:

In[1]:=1
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https://wolfram.com/xid/09bsqslje-j2fry1
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/09bsqslje-f3n4ql
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/09bsqslje-hqafox
Out[3]=3
Wolfram Research (2008), Equivalent, Wolfram Language function, https://reference.wolfram.com/language/ref/Equivalent.html.
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Wolfram Research (2008), Equivalent, Wolfram Language function, https://reference.wolfram.com/language/ref/Equivalent.html.

Text

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

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

CMS

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

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

APA

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

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

BibTeX

@misc{reference.wolfram_2025_equivalent, author="Wolfram Research", title="{Equivalent}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Equivalent.html}", note=[Accessed: 19-May-2025 ]}

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@misc{reference.wolfram_2025_equivalent, author="Wolfram Research", title="{Equivalent}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Equivalent.html}", note=[Accessed: 19-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_equivalent, organization={Wolfram Research}, title={Equivalent}, year={2008}, url={https://reference.wolfram.com/language/ref/Equivalent.html}, note=[Accessed: 19-May-2025 ]}

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@online{reference.wolfram_2025_equivalent, organization={Wolfram Research}, title={Equivalent}, year={2008}, url={https://reference.wolfram.com/language/ref/Equivalent.html}, note=[Accessed: 19-May-2025 ]}