# Definition:Precisely One Function

## Definition

Let $p_1, p_2, \ldots, p_n$ be statements.

The **precisely one function** is the propositional function $\map P {p_1, p_2, \ldots, p_n}$ defined as:

- $\map P {p_1, p_2, \ldots, p_n}$ is true if and only if
**precisely one**of $p_1, p_2, \ldots, p_n$ is true.

## Also see

- Results about
**the precisely one function**can be found here.

## Sources

- 1982: P.M. Cohn:
*Algebra Volume 1*(2nd ed.) ... (previous) ... (next): Chapter $1$: Sets and mappings: $\S 1.1$: The need for logic: Exercise $(6)$