## Venn Diagrams

**Venn Diagrams**

Often, when sorting objects or elements, it helps to look at the similarities and differences between groups. For example, if a parent has two children, the parent may be interested in activities that both children enjoy and can do together as well as activities that each child enjoys doing separately. A Venn diagram can help organize these activities by looking at one distinct circle for each child’s preferred activities, with the area where the circles overlap indicating common activities. This will help parents and other caregivers quickly reference which activities the children have in common and which they do not.

A Venn diagram provides a visual representation of two or more sets. For this Discussion, you will focus on two sets using a two-circle Venn diagram.

**Post 1**

- Using the letters from your first and last names, create a set and label it N. Sets do not contain duplicate letters, so if any letters are repeated in your name, only list them once in set N. For example, if your name is “Megan Ryan”, in roster form N = {m,e,g,a,n,r,y}. The letters, “A” and “N” in the last name, Ryan, are not written since they are written as part of the first name, Megan. The other set, M, will consist of the letters in the word “math” or M = {m,a,t,h}.
- Using a two-circle Venn diagram, list the elements that fall into Regions I, II, and III of the Venn diagram in roster notation. A worksheet containing a two-circle Venn diagram can be found here. Complete it and attach the Venn diagram to your post.
- Determine whether your sets are disjoint, subsets, equal sets, or overlapping sets and explain your reasoning.

Review an example of a response for this Discussion.

**Post 2**

Choose one of your classmate’s posts and:

- Check the accuracy of the sets N and M and make any necessary corrections.
- Assume the set N U M is the universal set. Choose and post one of the following:
- Write the set M’ in roster notation and describe what it represents.
- Write the set N’ in roster notation and describe what it represents.
- Write the set M U N’ in roster notation and describe what it represents.
- Write the set M in roster notation and describe what it represents.

Review an example of a response for this Discussion.

**Post 3**

- Share a scenario where a Venn diagram could be helpful in your personal or professional life.

OR

- There are many resources available for getting help in this course. Which resource(s) have you used? How did you use them? Which resource did you find most helpful? Which resource would you recommend for a struggling student? Why?

**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.

RESPONSE POST 1 Patrick:Patrick Hogan posted Jun 15, 2018 1:14 PM SubscribeThis page automatically marks posts as read as you scroll.Adjust automatic marking as read setting

RESPONSE POST2 PATRICK: The original post was:

**Name:** Barbara Blevins

**N=**{b, a, r, l, e, v, i, n, s}

**M=**{m, a, t, h}

**Region I=**{r, l, e, v, i, n, s}

**Region II=**{b, a}

**Region III=**{m, t, h}

While sets N and M are correct region II is incorrect. It should contain just the element of a since element b is not shared by set N and M. The corrected version should look like:

**N=**{b, a, r, l, e, v, i, n, s}

RESPONSE POST 3 PATRICK:A senario where a Venn Diagram could be useful would be determining where my girlfriend and I should eat for dinner. If I list all the places I want to eat that would create a set full of elements or restaurants (Set P) that I want. If she does the same that creates her set (Set A) and elements. Then we would just have to find the intersecting restaurants (P∩A) to determine the ideal restaurant to eat at. This is all ideal though as anyone with a girlfriend knows in the end we are going wherever she wants anyways!

RESPONSES2 BETHANY:N={b,e,t,h,a,n,y,o,d,g,s}

M={m,a,t,h}

Region I={b,e,n,y,o,d,g,s}

Region II={a,t,h}

Region III={m}

Sets N & M are over lapping sets because both sets must have elements in common to be overlapping sets (Angel, Runde, Abbott, 2013, pg 57).

1. Allen R. Angel, Christine D. Abbott, Dennis C. Runde, (2013), **A Survey of Mathematics with Applications 9th edition**, Pearson.MM150_Unit2_Worksheet.docx(43.9 KB)

REPONSES 2 POST2 BETHANY:Name: Steven Holmes

N={s,t,e,v,n,h,o,l,m}

M={m,a,t,h}

N U M={s,t,e,v,n,h,o,l,m,a}

Write the set M’ in roster notation and describe what it represents:

M’={s,e,v,n,o,l}

M’ represents all the elements in the universal set that are not included in set M.

RESPONSE2POST1 REBECCA:Name: Rebecca Reid

N= {r,e,b,c,a,i,d}

M= {m,a,t,h}

Region 1= {r,e,b,c,i,d}

Region 2= {a}

Region 3= {m,t,h}

Overlapping sets as they share the letter A