| Logical conjunction | |
| Other Titles: | AND |
| Venn Diagram: | Venn0001.svg |
| Definition: | xy |
| Truth Table: | (1000) |
| Logic Gate: | AND_ANSI.svg |
| Dnf: | xy |
| Cnf: | xy |
| Zhegalkin: | xy |
| 0-Preserving: | yes |
| 1-Preserving: | yes |
| Monotone: | no |
| Affine: | no |
| Self-Dual: | no |
In logic, mathematics and linguistics, and (
\wedge
\wedge
\&
K
x
⋅
\wedge
The and of a set of operands is true if and only if all of its operands are true, i.e.,
A\landB
A
B
An operand of a conjunction is a conjunct.[3]
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
\wedge
\&
x
⋅
&, &&, or and. In Jan Łukasiewicz's prefix notation for logic, the operator is K
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.
The conjunctive identity is true, which is to say that AND-ing an expression with true will never change the value of the expression. In keeping with the concept of vacuous truth, when conjunction is defined as an operator or function of arbitrary arity, the empty conjunction (AND-ing over an empty set of operands) is often defined as having the result true.