Definition:Disjunction

Disjunction is a binary connective written symbolically as $$p \or q$$ whose behaviour is as follows:


 * $$p \or q$$ is defined as: "either $$p$$ is true or $$q$$ is true or possibly both."

This is called the disjunction of $$p$$ and $$q$$.

The statements $$p$$ and $$q$$ are known as the disjuncts.

"$$p \or q$$ is voiced "$$p$$ or $$q$$".

The symbol $$\or$$ is also known as "vel" or "vee".

Complement
The complement of $$\or$$ is the NOR operator.

Truth Table
The truth table of $$p \or q$$ and its complement is as follows:

Boolean Interpretation
From the above, we see that the boolean interpretations for $$p \or q$$ are:

Notational Variants
Alternative symbols that mean the same thing as $$p \or q$$ are also encountered, for example:
 * $$p\ \texttt{OR}\ q$$
 * $$p + q$$

Note
This usage of "or", that allows the case where both disjuncts are true, is called inclusive or.

Compare exclusive or.