Encyclopedia > Disjunction

  Article Content

Logical disjunction

Redirected from Disjunction

In logic and mathematics, a disjunction is an "or statement". For example "John skis or Sally swims" is a disjunction.

Note that in everyday language, use of the word "or" can sometimes mean "either, but not both" (eg, "would you like tea or coffee?"). In logic, this is called an "exclusive disjunction" or "exclusive or". When used formally, "or" allows for both parts of the or statement (its disjuncts) to be true ("and/or").

The statement "P or Q" is often written as

PQ
Such a disjunction is false if both P and Q are false. In all other cases it is true.

For two inputs A and B, the truth table of the function is as follows.

 A B | A or B
 ----+--------
 F F |    F
 F T |    T
 T F |    T
 T T |    T

More generally a disjunction is a logical formula that can have one or more literals[?] separated only by ORs. A single literal is often considered to be a degenerate disjunction.

For example, all the following are disjunctions:

AB
¬AB
A ∨ ¬B ∨ ¬CD ∨ ¬E

The equivalent notion in set theory is the set theoretic union.

See also



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Wheatley Heights, New York

... or more races. 11.67% of the population are Hispanic or Latino of any race. There are 1,455 households out of which 43.6% have children under the age of 18 living wi ...

 
 
 
This page was created in 35.2 ms