# Exclusive Or/Examples/Monday or Not Monday

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## Example of Exclusive Or

The following is an example of an exclusive or statement:

*Either today is Monday or today is not Monday.*

## Proof

By the Law of Excluded Middle, *today is Monday* or *today is not Monday* is a truth.

By the Principle of Non-Contradiction, *today is Monday* and *today is not Monday* is a falsehood.

Hence the result by definition of exclusive or.

$\blacksquare$

## Sources

- 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... Example $1.1.1$