Definition:Exclusive Or/Truth Table

Definition

The characteristic truth table of the exclusive or operator $p \oplus q$ is as follows:

$\begin{array}{|cc||c|} \hline p & q & p \oplus q \\ \hline \F & \F & \F \\ \F & \T & \T \\ \T & \F & \T \\ \T & \T & \F \\ \hline \end{array}$

Matrix Form

$\begin{array}{c|cc} \oplus & \T & \F \\ \hline \T & \F & \T \\ \F & \T & \F \\ \end{array}$

Truth Table Number

The truth table number of the exclusive or operator $p \oplus q$ is as follows:

Ascending and descending order:

$0110$ or $\F \T \T \F$

Sources

• 1959: A.H. Basson and D.J. O'Connor: Introduction to Symbolic Logic (3rd ed.) ... (previous) ... (next): $\S 2.5$: Further Logical Constants
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): exclusive disjunction, exclusive or or non-equivalence
• 1993: M. Ben-Ari: Mathematical Logic for Computer Science ... (previous) ... (next): Chapter $2$: Propositional Calculus: $\S 2.1$: Boolean operators
• 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $1$: Elementary, my dear Watson: $\S 1.1$: You have a logical mind if...
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): exclusive disjunction