Logical conjunction

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

A logical conjunction of propositions $$p$$ and $$q$$ may be written in various ways. Among the most common are these:


 * $$p ~\mathrm{and}~ q$$
 * $$p \land q$$
 * $$p \cdot q$$
 * $$p~q$$
 * $$pq$$

A truth table for $$p \land q$$ appears below:

A logical graph for $$p \land q$$ is drawn as two letters attached to a root node:

Written as a string, this is just the concatenation $$pq.$$ The proposition $$pq$$ may be taken as a Boolean function $$f(p, q)$$ having the abstract type $$f : \mathbb{B} \times \mathbb{B} \to \mathbb{B},$$ where $$\mathbb{B} = \{ 0, 1 \}$$ is interpreted in such a way that $$0$$ means $$\mathrm{false}$$ and $$1$$ means $$\mathrm{true}.$$

A Venn diagram for $$p \land q$$ indicates the region, in this case a single cell, where $$pq$$ is true by means of a distinct color or shading, as shown below:

Focal nodes

 * Inquiry Live
 * Logic Live

Peer nodes

 * Logical Conjunction @ InterSciWiki
 * Logical Conjunction @ Subject Wikis
 * Logical Conjunction @ Wikiversity
 * Logical Conjunction @ 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 Conjunction, InterSciWiki
 * Logical Conjunction, Wikiversity
 * Logical Conjunction, Wikiversity Beta
 * Logical Conjunction, Wikipedia