Exclusive Or/Examples

From ProofWiki
Jump to navigation Jump to search

Examples of Exclusive Or

Monday or Not Monday

The following is an example of an exclusive or statement:

Either today is Monday or today is not Monday.


One of Five Statements is True

Which of the following $5$ statements is true?

$(1): \quad$ Exactly one of these statements is false.
$(2): \quad$ Exactly two of these statements are false.
$(3): \quad$ Exactly three of these statements are false.
$(4): \quad$ Exactly four of these statements are false.
$(5): \quad$ Exactly five of these statements are false.


Tea or Coffee

Consider the sentence that may be found on the table d'hote menu of a restaurant:

Breakfast includes either tea or coffee.

It is usually taken for granted that this is an example of an exclusive or statement:

The diner may include either tea with breakfast, or coffee with breakfast, but not both.

The usual understanding is that if the diner wishes both, then extra is to be paid.