Question:
Answer each of the following questions by writing an expression using set theory notation but without using plain English, without using set-builder notation, without introducing any new variables, and without using propositional or first-order logic.
Let's say that a committee is a group of people, which we can think of as being represented by the set of people that comprise it. Let's have $S$ represent the set of all students at a school and let $F$ represent the set of all faculty at the school. Write an expression representing the set of all committees you can make from school students and faculty that contain one student and at least one faculty member. You can assume no one is both a student and a faculty member.
My working:
$\mathscr P (S \cup T) – $ ($\mathscr P (S) \cup \mathscr P (T) $)
Now i'm not sure if this is correct, as it took me quite some time to reach this conclusion. And if anyone has a different way of writing this please feel to write it down below as I've been looking for other ways to solve this.
Best Answer
You probably meant ($F$ for faculty, not $T$):
$$\mathscr P (S \cup F) - \left(\mathscr P (S) \cup \mathscr P (F) \right)$$
and this is the right answer: the total population is $S \cup F$ and we want all subsets of that, but we want to disregard those that are entirely a subset of either $S$ or $F$. Well done.