Definition:Disjunction

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


 * $p \lor q$

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
 * the members of the disjunction.

$p \lor q$ is voiced:
 * $p$ or $q$

Also known as
The disjunction is also known as the logical sum.

The disjuncts are thence known as the summands of the logical sum.

The symbol $\lor$ comes from the first letter of the Classical Latin vel.

This usage of or, that allows the case where both disjuncts are true, is called inclusive or, or the inclusive disjunction. In natural language the term and/or is often seen, especially in the case of legal documents.

Some sources refer to this as the weak or, where the strong or is used in the sense of the exclusive or.

$p \lor q$ is also called the logical alternation, or just alternation, of $p$ and $q$.

Also see

 * Definition:Subcontrary Statements


 * Definition:Exclusive Or