Logical conjunction

In logic, mathematics and linguistics, and (${\displaystyle \wedge }$) is the truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as ${\displaystyle \wedge }$ or ${\displaystyle \&}$ or ${\displaystyle K}$ (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., ${\displaystyle A\land B}$ is true if and only if ${\displaystyle A}$ is true and ${\displaystyle B}$ is true.

An operand of a conjunction is a conjunct.

Beyond logic, the term "conjunction" also refers to similar concepts in other fields:

And is usually denoted by an infix operator: in mathematics and logic, it is denoted by a "wedge" ${\displaystyle \wedge }$ (Unicode U+2227 ∧ LOGICAL AND), ${\displaystyle \&}$ or ${\displaystyle \times }$; in electronics, ${\displaystyle \cdot }$; and in programming languages &, &&, or and. In Jan Łukasiewicz's prefix notation for logic, the operator is ${\displaystyle K}$, for Polish koniunkcja.

In mathematics, the conjunction of an arbitrary number of elements ${\displaystyle a_{1},\ldots ,a_{n}}$ can be denoted as an iterated binary operation using a "big wedge" ⋀ (Unicode U+22C0 ⋀ N-ARY LOGICAL AND):

${\displaystyle \bigwedge _{i=1}^{n}a_{i}=a_{1}\wedge a_{2}\wedge \ldots a_{n-1}\wedge a_{n}}$

In classical logic, 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 (also known as iff) both of its operands are true.