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).

REFERENCES:

Carnap, R. Introduction to Symbolic Logic and Its Applications. New York: Dover, pp. 7 and 10, 1958.

Mendelson, E. Introduction to Mathematical Logic, 4th ed. London: Chapman & Hall, p. 12, 1997.

Simpson, R. E. "The AND Gate." §12.5.2 in Introductory Electronics for Scientists and Engineers, 2nd ed. Boston, MA: Allyn and Bacon, pp. 538 and 544-546, 1987.

Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, p. 871, 2002.