A tale of why you (U, that is) needs a tail

What is this collection of symbols?

No, it is not a wallpaper border pattern, a brain teaser, or ancient hieroglyphics. It is a set identity, of course!

{C\cap U\subset C\cup U}

When I was in college I had a math major friend who said that all he learned in our topology class was to put tails on his U’s so that they didn’t look like unions. (I’m sure he was selling himself short—he was a very bright, if unmotivated, student.)

I mentioned this comment to my topology class last week. The class is run using the Moore method, so the students present all of the material at the board. We often use U’s’s to represent open sets. So now, several times per class a student note-taker tells the student lecturer, “please add tails to your U’s.”