In this series, I’m compiling some of the quips and one-liners that I’ll use with my students to hopefully make my lessons more memorable for them.

Here’s a problem that might arise in my discrete mathematics class:

Find the negation of .

This requires a couple of reasonably complex steps. First, we use the fact that is logically equivalent to $\lnot p \lor q$:

.

Next, we have to apply DeMorgan’s Law to find the negation:

Finally, we arrive at the final step: simplifying . At this point, I tell my class, it’s a bit of joke, especially after the previous, more complicated steps. “Not not ,” of course, is the same as . So this step is a bit of a joke. Which steps up the following cringe-worthy pun:

In fact, you might even call this a not-not joke.

After the groans settle down, we finish the derivation:

.