Definition:Exclusive Or/Also known as

Exclusive Or: Also known as

This usage of or, that disallows the case where both disjuncts are true, is also called:

• exclusive disjunction
• logical inequality
• non-equivalence
• symmetric difference
• the alternative function
• aut (from the Latin), pronounced out.

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

In natural language, when it is necessary to be precise about the nature of the term being used, the phrase but not both is often employed.

Some sources give the symbol as $\underline \lor$ or $\not \equiv$

Sources

• 1959: A.H. Basson and D.J. O'Connor: Introduction to Symbolic Logic (3rd ed.) ... (previous) ... (next): $\S 2.5$: Further Logical Constants
• 1973: Irving M. Copi: Symbolic Logic (4th ed.) ... (previous) ... (next): $2$ Arguments Containing Compound Statements: $2.1$: Simple and Compound Statements
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): aut
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): exclusive disjunction, exclusive or or non-equivalence
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): disjunction (alternation)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): disjunction (alternation)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): exclusive disjunction