AND
A connective in logic which yields true if all conditions are true,
and false if any condition is false.
AND 
is denoted 
(Mendelson
1997, p. 12), 
, 
(Simpson 1987, p. 538), 
, 
(Carnap 1958,
p. 7), or simply 
(Simpson 1987, p. 538). The way
to distinguish the similar symbols 
(AND) and 
(OR) is to note
that the symbol for AND is oriented in the same direction as the capital letter 'A.'
The AND operation is implemented in the Wolfram
Language as And[A,
B, ...]. The circuit diagram symbol for an AND gate is illustrated above.
The AND operation (
) can be written in terms of NOT
(!) and OR (
) as
 |
The binary AND operator has the following truth table (Carnap 1958, p. 10; Simpson 1987, p. 545; Mendelson 1997, p. 12).
 |  |  |
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
A product of ANDs (the AND of 
conditions) is
called a conjunction, and is denoted
 |
For example, the truth table for 
AND 
AND 
is given below
(Simpson 1987, p. 545).
 |  |  |  |
| T | T | T | T |
| T | T | F | F |
| T | F | T | F |
| T | F | F | F |
| F | T | T | F |
| F | T | F | F |
| F | F | T | F |
| F | F | F | F |
Two binary numbers can have the operation AND performed bitwise with 1 representing true and 0 false. Some computer
languages denote this operation on 
, 
, and 
as A &&
B && C or logand(A,B,C). Bitwise AND is implemented in the
Wolfram Language as BitAnd[n1,
n2, ...]. The illustration above plots the bitwise AND of the array of numbers
from 
to 31 (Wolfram 2002, p. 871).
Contact the MathWorld Team
and
