In logic and mathematics, logical conjunction or and is a twoplace logical connective that has the value true if both of its operands are true, otherwise a value of false.
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And is usually expressed with an infix operator. In mathematics and logic, it is usually ∧; in electronics ; and in programming languages, & or and. Some programming languages have a related control structure, the shortcircuit and, written &&, and then, etc.
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.
The truth table of p AND q:
p  q  ∧ 

T  T  T 
T  F  F 
F  T  F 
F  F  F 
The Venn diagram of "A and B" (the red area is true)
The analogue of conjunction for a (possibly infinite) family of statements is universal quantification, which is part of predicate logic.
As a rule of inference, conjunction introduction is a classically valid, simple argument form. The argument form has two premises, A and B. Intuitively, it permits the inference of their conjunction.
or in logical operator notation:
Here is an example of an argument that fits the form conjunction introduction:
Conjunction elimination is another classically valid, simple argument form. Intuitively, it permits the inference from any conjunction of either element of that conjunction.
...or alternately,
In logical operator notation:
...or alternately,
The following properties apply to conjunction:
If using binary values for true (1) and false (0), then logical conjunction works exactly like normal arithmetic multiplication.
In highlevel 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
"&
". Many languages also provide shortcircuit control
structures corresponding to logical conjunction.
Logical conjunction is often used for bitwise operations, where
0
corresponds to false and 1
to true:
0 AND 0
= 0
,0 AND 1
= 0
,1 AND 0
= 0
,1 AND 1
= 1
.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:
11000110 AND 10100011
=
10000010
.This can be used to select part of a bitstring using a bit mask. For
example, 10011101 AND
00001000
=
00001000
extracts the fifth bit of an
8bit 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 CurryHoward correspondence relates logical conjunction to product types.
The intersection used in set theory is defined in terms of a logical conjunction: x ∈ A ∩ B if and only if (x ∈ A) ∧ (x ∈ B). Because of this, settheoretic intersection shares several properties with logical conjunction, such as associativity, commutativity, and idempotence.
The logical conjunction and in logic 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. For example, "They got married and had a child" in common discourse means that the marriage came before the child. The word "and" can also imply a partition of a thing into parts, as "The American flag is red, white, and blue." Here it is not meant that the flag is at once red, white, and blue, but rather that it has a part of each color.

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Logical conjunction (very often called and) is a Logic operation. Usually it takes two inputs. It is true, when both inputs are true. Otherwise it is false.
