Equivalent
Equivalent[e1,e2,…]
represents the logical equivalence e1⇔e2⇔…, giving True when all of the ei are the same.
Details
- Equivalent[e1,e2,…] can be input in StandardForm and InputForm as e1⇔e2⇔…. The character ⇔ can be entered as
equiv
or \[Equivalent]. - As a Boolean function, Equivalent[e1,e2,…] is equivalent to (e1∧e2∧⋯)∨(¬e1∧¬e2∧⋯).
Examples
open all close all
:Scope (2)
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:
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