The logical connective of this operator is typically represented as

[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 a "wedge"

In Jan Łukasiewicz's prefix notation for logic, the operator is

[4] In mathematics, the conjunction of an arbitrary number of elements

can be denoted as an iterated binary operation using a "big wedge" ⋀ (Unicode U+22C0 ⋀ N-ARY LOGICAL AND):[5]

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.

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.

:[1][2] In systems where logical conjunction is not a primitive, it may be defined as[6] It can be checked by the following truth table (compare the last two columns): or It can be checked by the following truth table (compare the last two columns): As a rule of inference, conjunction introduction is a classically valid, simple argument form.

Intuitively, it permits the inference of their conjunction.

or in logical operator notation, where \vdash expresses provability: Here is an example of an argument that fits the form conjunction introduction: Conjunction elimination is another classically valid, simple argument form.

In terms of the object language, this reads This formula can be seen as a special case of when

Either of the above are constructively valid proofs by contradiction.

commutativity: yes associativity: yes[7] distributivity: with various operations, especially with or with exclusive or: with material nonimplication: with itself: idempotency: yes monotonicity: yes truth-preserving: yesWhen all inputs are true, the output is true.

Walsh spectrum: (1,-1,-1,1) Nonlinearity: 1 (the function is bent) If using binary values for true (1) and false (0), then logical conjunction works exactly like normal arithmetic multiplication.

In high-level computer programming and digital electronics, logical conjunction is commonly represented by an infix operator, usually as a keyword such as "AND", an algebraic multiplication, or the ampersand symbol & (sometimes doubled as in &&).

Many languages also provide short-circuit control structures corresponding to logical conjunction.

Logical conjunction is often used for bitwise operations, where 0 corresponds to false and 1 to true: The operation can also be applied to two binary words viewed as bitstrings of equal length, by taking the bitwise AND of each pair of bits at corresponding positions.

For example: This can be used to select part of a bitstring using a bit mask.

For example, 10011101 AND 00001000  =  00001000 extracts the fourth bit of an 8-bit bitstring.

In computer networking, bit masks are used to derive the network address of a subnet within an existing network from a given IP address, by ANDing the IP address and the subnet mask.

Logical conjunction "AND" is also used in SQL operations to form database queries.

The Curry–Howard correspondence relates logical conjunction to product types.

The membership of an element of an intersection set in set theory is defined in terms of a logical conjunction:

Through this correspondence, set-theoretic intersection shares several properties with logical conjunction, such as associativity, commutativity and idempotence.

As with other notions formalized in mathematical logic, the logical conjunction and is related to, but not the same as, the grammatical conjunction and in natural languages.

English "and" has properties not captured by logical conjunction.

For example, "and" sometimes implies order having the sense of "then".

The word "and" can also imply a partition of a thing into parts, as "The American flag is red, white, and blue."