Sets and proving sets

Use only the definitions for element of, not an element of, subset of, not a subset of, union, intersection, set complement, set difference and other

definitions provided in this quiz. Do not use any prior results UNLESS it is a result you proved in an earlier problem in THIS QUIZ. Indicate where your proof

or counterexample begins. Use grammatically correct English and proper capitalization and punctuation. Leave NOTHING to my imagination. If you wonder whether

you should write something, you probably should write it. Your reader should not need to perform any calculations or make any inferences.

Sample Solution