# List all the proper subsets of your universal set. Are all subsets of a set also proper subsets of a set? Why or why not?

**Sets and Subsets**

The ability to classify items into sets is important in many contexts. For example, the registrar of a university puts students into classes. Each class can be considered a set. It can also be considered a subset of the entire student population. The admissions officer puts students into majors. Again, each major can be considered a subset of the entire student population. At graduation, students need to be put into groups with similar GPAs for honors, groups with similar degrees, or groups from different schools within the university. On this Unit’s Discussion Board, you will investigate sets, subsets, and proper subsets making at least three posts as described below.

**Post 1**

- Using your first, middle, and last name, create a universal set and write it in roster notation. If you do not have a middle name, use your first and last name only.
- List all the subsets of your universal set.
- How many subsets did you list? How do you know how many subsets a set will have?
- List all the proper subsets of your universal set. Are all subsets of a set also proper subsets of a set? Why or why not?

Review an example of a response for this Discussion.

**Post 2**

- Choose one of your classmates’ posts and using the letters of either their first, middle or last name, create a set and write it in roster notation.
- Determine the number of distinct subsets of the set.
- Determine the number of distinct proper subsets of the set.

Review an example of a response for this Discussion

**Post 3**

- Watch the video, “How to Learn Math: Four Key Messages” found here:https://www.youcubed.org/resources/four-boosting-messages-jo-students/. Share something from the video that you think is helpful. How do you think it can help you in this class?

**Discussion Guidelines**

In this unit’s Discussion, you will interact with your classmates on the course content. Remember, your goal for Discussion Assignments is to ensure that:

- Responses are on topic, original, and contribute to the quality of the Discussion.
- Responses make frequent, informed references to unit material.
- Responses are clearly written.
- You submit two or more Discussion Board responses to classmates as described in the Discussion Question that are thoughtful and advance the Discussion.

Keep in mind that when you post, you should include references to the textbook and any material found online. The class is all about sharing knowledge, so use Discussions as a way of creating a community resource for yourself and your classmates.

Please response to patrick post:

Name: Patrick Michael Hogan

Universal Set:

U={Patrick,Michael,Hogan}

Subsets:

{Patrick,Michael,Hogan}, {Patrick,Michael}, {Patrick,Hogan}, {Michael, Hogan}, {Patrick}, {Michael}, {Hogan}, {}

There are 8 Subsets.

Proper Subsets:

{Patrick,Michael}, {Patrick, Hogan}, {Michael, Hogan}, {Patrick}, {Michael}, {Hogan}, {}

Not every subset of a set is a proper set. This can be seen in the example from the book which states “consider C = {car, bus, train} and D = {train, car, bus}. Set C is a subset of set D, C ⊆ D, because every element of set C is also an element of set D. Set C, however, is not a proper subset of set D, C ⊄ D, because set C and set D are equal sets.”

Please also response to Nona:

Name: Nona Ann Foga

Universal Set: U= {Nona, Ann, Foga}

Subsets: {Nona, Ann, Foga}, {Nona, Ann} {Nona, Foga}, {Ann, Foga}, {Nona}, {Ann}, {Foga}, {}

Proper Subsets: {Nona, Ann}, {Nona, Foga}, {Ann, Foga}, {Nona}, {Ann}, {Foga}, {}

(Hope this what you’re asking for?)