Logical equality

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Logical equality is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both operands are false or both operands are true.

The truth table of $p\mathrm{EQ}q,$ also written $p=q,$ $p\iff q,$ or $p\equiv q,$ appears below:

$\text{Logical Equality}$

$p$	$q$	$p=q$
$\mathrm{F}$	$\mathrm{F}$	$\mathrm{T}$
$\mathrm{F}$	$\mathrm{T}$	$\mathrm{F}$
$\mathrm{T}$	$\mathrm{F}$	$\mathrm{F}$
$\mathrm{T}$	$\mathrm{T}$	$\mathrm{T}$

Syllabus

Focal nodes

• Inquiry Live
• Logic Live

Peer nodes

• Logical Equality @ InterSciWiki
• Logical Equality @ Subject Wikis
• Logical Equality @ Wikiversity
• Logical Equality @ Wikiversity Beta

Logical operators

• Exclusive disjunction
• Logical conjunction
• Logical disjunction
• Logical equality

• Logical implication
• Logical NAND
• Logical NNOR
• Negation

Related topics

• Ampheck
• Boolean domain
• Boolean function
• Boolean-valued function
• Differential logic

• Logical graph
• Minimal negation operator
• Multigrade operator
• Parametric operator
• Peirce's law

• Propositional calculus
• Sole sufficient operator
• Truth table
• Universe of discourse
• Zeroth order logic

Relational concepts

• Continuous predicate
• Hypostatic abstraction
• Logic of relatives
• Logical matrix

• Relation
• Relation composition
• Relation construction
• Relation reduction

• Relation theory
• Relative term
• Sign relation
• Triadic relation

Information, Inquiry

• Inquiry
• Dynamics of inquiry

• Semeiotic
• Logic of information

• Descriptive science
• Normative science

• Pragmatic maxim
• Truth theory

Related articles

• Cactus Language
• Futures Of Logical Graphs
• Propositional Equation Reasoning Systems

• Differential Logic : Introduction
• Differential Propositional Calculus
• Differential Logic and Dynamic Systems

• Prospects for Inquiry Driven Systems
• Introduction to Inquiry Driven Systems
• Inquiry Driven Systems : Inquiry Into Inquiry

Document history

Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.

• Logical Equality, InterSciWiki
• Logical Equality, Wikinfo
• Logical Equality, Wikiversity
• Logical Equality, Wikiversity Beta
• Logical Equality, Wikipedia