Equivalent

Equivalent[e1,e2,…]

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

Details

Examples

open allclose all

Basic Examples  (2)

Test equivalence of Boolean expressions:

Enter using equiv:

Scope  (2)

Automatic simplifications:

TraditionalForm formatting:

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_2023_equivalent, author="Wolfram Research", title="{Equivalent}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Equivalent.html}", note=[Accessed: 04-October-2023 ]}

BibLaTeX

@online{reference.wolfram_2023_equivalent, organization={Wolfram Research}, title={Equivalent}, year={2008}, url={https://reference.wolfram.com/language/ref/Equivalent.html}, note=[Accessed: 04-October-2023 ]}