The notation of set theory (e.g. ,,,,,,=, etc.) is a great tool for describing the real world. 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 (which well cover next week). No justification is required.

1. Let C be the set of all cats and D be the set of all dogs. Let A be the set of all adorable things and B be the set of all bouncy things. Write an expression that says "all cats and all dogs are both adorable and bouncy."

2. Suppose youre on an exciting first date. Let Y represent the set of all your hobbies and D represent the set of all your dates hobbies. Write an expression that says that you have a hobby that your date doesnt have.

3. Lets 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. Lets have S represent the set of all students at Stanford and let F represent the set of all faculty at Stanford. Write an expression representing the set of all committees you can make from Stanford students and faculty that contain at least one student and at least one faculty member. You can assume no one is both a student and a faculty member.