Editing Vacuous truth (section)

== Examples ==
These examples, one from [[mathematics]] and one from [[natural language]], illustrate the concept of vacuous truths:

* "For any integer ''x'', if {{nowrap|''x'' > 5}} then {{nowrap|''x'' > 3}}."<ref>{{Cite web|url=https://math.stackexchange.com/questions/734418/what-precisely-is-a-vacuous-truth|title=logic – What precisely is a vacuous truth?|website=Mathematics Stack Exchange}}</ref> – This statement is [[Truth|true]] non-vacuously (since some [[integer]]s are indeed greater than 5), but some of its implications are only vacuously true: for example, when ''x'' is the integer 2, the statement implies the vacuous truth that "if {{nowrap|2 > 5}} then {{nowrap|2 > 3}}".
* "All my children are goats" is a vacuous truth when spoken by someone without children. Similarly, "None of my children is a goat" would also be a vacuous truth when spoken by the same person.