Homework Help: Discrete Mathematics - Operations with Sets within sets.

1. Jul 26, 2012

johnstobbart

Hello to everyone on this site. This is my first post and I hope to be on here more often in the coming years. I want to clear a few things up involving operations with subsets of sets (I'm not sure if this is a more correct term, an example would be Set B below).

The problem statement, all variables and given/known data

We have the following sets:
U = {1, 2, 3, 4, 5, ∅, {1}},
A = {1, 3}
B = {{1}, 1}
C = {2, 4}
D = {∅, 1, 2}

2. Relevant equations

1. D + B (with + meaning symmetric set difference)
2. B - D (with - meaning set difference)
3. A' (complement of A)
4. Is {∅, {1}} ∈ U? Why?

3. The attempt at a solution

1. D + B would probably be {∅, {1}, 2}
2. I think B - D would be {{1}}
3. A' = {{1}, 2, 4, 5, ∅}
4. It is not an element of U because it is a subset of U.

Thank you for the help in advance. I have seen similar questions on the web, but I can't find much information about working with sets such as B (maybe I didn't look hard enough or understand correctly). My textbook contains no information about it either. I find the set {1} within B a bit confusing.