# Equivalent

Equivalent[e1,e2,]

represents the logical equivalence e1e2, giving True when all of the ei are the same.

# Examples

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## Basic Examples(2)

Test equivalence of Boolean expressions:

Enter using equiv:

## Scope(2)

Automatic simplifications:

## Applications(1)

Prove equivalence between different Boolean expressions:

## Properties & Relations(7)

Truth table for binary Equivalent:

Ternary Equivalent:

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

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

This proves that the two representations are indeed equivalent:

Equivalent can be represented in terms of BooleanCountingFunction:

Equivalent with two arguments is equivalent to Xnor:

For more arguments, these are different primitives:

Use Resolve to prove equivalence of two systems of equations:

Equivalent is effectively Equal for Boolean expressions:

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.

#### CMS

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

#### BibTeX

@misc{reference.wolfram_2024_equivalent, author="Wolfram Research", title="{Equivalent}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Equivalent.html}", note=[Accessed: 16-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_equivalent, organization={Wolfram Research}, title={Equivalent}, year={2008}, url={https://reference.wolfram.com/language/ref/Equivalent.html}, note=[Accessed: 16-August-2024 ]}