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
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:
A ∨ B
¬A ∨ B
A ∨ ¬B ∨ ¬C ∨ D ∨ ¬E
The equivalent notion in set theory is the set theoretic union.