Exclusive Or/Examples/Monday or Not Monday

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 $1.1.1$
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