It is weird to think about jackass middle school children leveraging a concept they likely have not learned about and perhaps never will. But it happens to be true. When a teacher tells a student "no running in the halls" a smartass doesn't see this as a rule but as an opportunity. A teacher means to imply no running in all the places where it may be dangerous including the halls, but the smartass hears that they may run in all places except the halls. The enterprising smartass will immediately put this to the test by running in a classroom, a stairwell, or on the roof.

A smartass can not help but test the logically flawed rule the teacher has made. In our example running on the roof is following the rule and a smartass must use this as a flex to put the teacher in their place. The rule as constructed by the teacher is the proposition P "if in the hall" and the conclusion Q "running is not permitted." When P is false there's nothing the statement logically says about running, so by running on the roof the statement is true and the rule has been followed. Obviously, this smartass student deserves praise for following the rules. Not so fast smart guy!

To the student's dismay, this behavior is rarely praised. The teacher implicitly knows, as do most responsible adults, that the rule was only followed because in the case of running on the roof (i.e. not in the hall) the statement is vacuously true and rules followed vacuously are subject to another rule: smartasses will be disciplined.

The fun with vacuous truths never ends. Consider the statement "I do all my murders with that knife." If I was being interrogated by the police and they brought a knife to the interrogation room to demand I admit to killing someone with the knife I would instinctively want to respond:

I do all my murders with that knife!

It would be so tempting. Thankfully as an adult, I've learned the hard way that smartasses will be disciplined. Indeed it will be better for everyone involved if I do what any good lawyer would instruct and don't talk to the police.

I know I've picked a crass example, but it makes this all the more fun since the statement at face value would be so shocking. Not only did I murder with the knife, but I've confessed to multiple murders. Cops, like teachers, don't appreciate clever smartasses and have certainly never been introduced to the universal quantifier.

This little joke would probably force me to attempt teaching mathematical logic to the police, jury, and parole board. All the while I could take solace in how clever I was in phrasing my denial while sitting in my prison cell.

The domain of discourse that I constructed is the set M of every murder I've committed, since I've never committed a murder M is empty, thus it is true that all the murders were done with the knife because I've never murdered.

It is also true that I always murder on Tufurnetherwanday (the day between Tuesday and Wednesday) at precisely the 25th hour in the township of New Smartassastan.