A connective in logic which yields true if any one of a sequence conditions is true, and false if all conditions are false. In formal logic, the term disjunction (or, more specifically, inclusive disjunction) is commonly used to describe the OR operator.  OR  is denoted  (Mendelson 1997, p. 13), ,  (Simpson 1987, p. 539), or  (Simpson 1987, p. 539). The circuit diagram symbol for an OR gate is illustrated above.

The symbol  derives from the first letter of the Latin word "vel," meaning "or," and the expression  is voiced either " or " or " vel ." 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 OR operation is implemented in the Wolfram Language as Or[A, B, ...].

The OR operation can be written in terms of NOT and AND as

(Mendelson 1997, p. 26).

The binary OR operator has the following truth table (Carnap 1958, p. 10; Simpson 1987, p. 542; Mendelson 1997, p. 13).

T	T	T
T	F	T
F	T	T
F	F	F

A product of ORs is called a disjunction and is denoted

For example, the truth table for the ternary OR operator is shown below (Simpson 1987, p. 543).

T	T	T	T
T	T	F	T
T	F	T	T
T	F	F	T
F	T	T	T
F	T	F	T
F	F	T	T
F	F	F	F

A bitwise version of OR can also be defined that performs a bitwise OR on the binary digits of two numbers  and  and then converts the resulting binary number back to decimal. Bitwise OR is sometimes denoted  and is implemented in the Wolfram Language as BitOr[n1, n2, ...]. The illustration above plots the bitwise OR 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. 13, 1997.

Simpson, R. E. "The OR Gate." §12.5.1 in Introductory Electronics for Scientists and Engineers, 2nd ed. Boston, MA: Allyn and Bacon, pp. 542-544, 1987.

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