# critical thinking set theory

Hello,

I need some assistance with a math problem using set theory and creating a Venn diagram.

The problem is: A survey of 500 adults was conducted to determine why more undergraduate students do not pursue degrees in science, technology, engineering, and math (STEM). The results of the survey show that 250 respondents believed that students do not pursue STEM degrees because the subjects are too difficult, while 105 respondents believed it is because the subjects do not have applications in their careers. There were ten respondents who believed both, difficulty and lack of applications, were the reasons why no more students pursue STEM degrees.

The assignment is broken down into two parts.

__Part I: Complete the following steps:__

- Define two sets to represent the two different opinions of the surveyâ€™s respondents.
- Create a Venn diagram to represent the results of this survey.
- How many respondents believed students do not pursue STEM degrees only because the subjects are too difficult?
- How many respondents believed students do not pursue STEM degrees only because the subjects do not have applications in their careers?
- How many respondents believed that neither the difficulty nor the lack of applications of the subjects are reasons why students do not pursue STEM degrees?

The second part is answering the questions in a 2 page APA formatted paper with references to support.

__Part II: Based on your work in Part I, discuss the following:__

- Use an alternative method to define the sets in Part I.
- Explain how you created the Venn diagram. Describe how you found the numbers corresponding to each region.
- Discuss how you can use set operations to answer questions three through five in Part I.
- Discuss how the numbers on the Venn diagram would have changed if the total respondents who believed students do not pursue STEM degrees because of the lack of applications increased to 250. What would this imply for the answers to questions three through five in Part I?
- Discuss the advantages of using a Venn diagram to analyze the results of this survey.
- Provide an example of a real-world survey that could be modeled using the Venn diagram below.

Please answer within 4 hours. Thank You!!