Logical conjunction

In <a href="/facts/Logic/8JnpJLtt">logic</a>, <a href="/facts/Mathematics/pxTouaz4">mathematics</a> and <a href="/facts/Linguistics/oQuamvf2">linguistics</a>, and (
 
 
 
 ∧
 
 
 {\displaystyle \wedge }
 
) is the <a href="/facts/Truth_function/aH5kBhQ7">truth-functional</a> operator of conjunction or logical conjunction. The <a href="/facts/Logical_connective/VkPhUs6M">logical connective</a> of this operator is typically represented as 
 
 
 
 ∧
 
 
 {\displaystyle \wedge }
 
 or 
 
 
 
 &
 
 
 {\displaystyle \&}
 
 or 
 
 
 
 K
 
 
 {\displaystyle K}
 
 (prefix) or 
 
 
 
 ×
 
 
 {\displaystyle \times }
 
 or 
 
 
 
 ⋅
 
 
 {\displaystyle \cdot }
 
 in which 
 
 
 
 ∧
 
 
 {\displaystyle \wedge }
 
 is the most modern and widely used.
The and of a set of operands is true if and only if all of its operands are true, i.e., 
 
 
 
 A
 ∧
 B
 
 
 {\displaystyle A\land B}
 
 is true if and only if 
 
 
 
 A
 
 
 {\displaystyle A}
 
 is true and 
 
 
 
 B
 
 
 {\displaystyle B}
 
 is true.
An operand of a conjunction is a conjunct.
Beyond logic, the term "conjunction" also refers to similar concepts in other fields:

<ul><li>In <a href="/facts/Natural_language/B4gLS7Kd">natural language</a>, the <a href="/facts/Denotation/oABEtLtA">denotation</a> of expressions such as <a href="/facts/English_language/tpkxGt7b">English</a> "<a href="/facts/Conjunction_(grammar)/bKVVIpob">and</a>";</li>
<li>In <a href="/facts/Programming_language/cWTYbgWa">programming languages</a>, the <a href="/facts/Short-circuit_evaluation/GYhompFd">short-circuit and</a> <a href="/facts/Control_flow/2XTDfErC">control structure</a>;</li>
<li>In <a href="/facts/Set_theory/1ptfsvUP">set theory</a>, <a href="/facts/Intersection_(set_theory)/RPfUNJh9">intersection</a>.</li>
<li>In <a href="/facts/Lattice_(order)/5ak6ufky">lattice theory</a>, logical conjunction (<a href="/facts/Infimum_and_supremum/oXCKVopz">greatest lower bound</a>).</li></ul>

Logical conjunction open-in-new

Logical conjunction