Inclusive disjunction

For the other uses, see Disjunction.

Inclusive disjunction (also called or) is a logic operation. It normally takes two truth values as inputs and returns one truth value as output. It is false when both inputs are false, but is true otherwise. It is written with the symbol ${\displaystyle \lor }$.^[1]

Venn diagram of ${\displaystyle \scriptstyle A\lor B}$

Venn diagram of ${\displaystyle \scriptstyle A\lor B\lor C}$

In general, given two propositions ${\displaystyle A}$ and ${\displaystyle B}$, ${\displaystyle A\lor B}$ is true if ${\displaystyle A}$ is true, or if ${\displaystyle B}$ is true, or if both ${\displaystyle A}$ and ${\displaystyle B}$ are true.^[2]

This is different from the exclusive disjunction, which asserts "either x or y, but not both".^[3]

Related pages

• Alternative
• Boolean algebra
• Horn clause
• Logical conjunction
• XOR gate