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4 pages/β‰ˆ1100 words
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Style:
APA
Subject:
Mathematics & Economics
Type:
Essay
Language:
English (U.S.)
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Topic:

Understanding Sets and Subsets and the Union and Intersection of Sets

Essay Instructions:

1. Let A = {l,m,n,o,p}, B = {o,p,q,r}, and C = {r,s,t,u}. Find the following:
(A ∪ B) ∩ C
A ∩ (C ∪ B)
(A ∩ B) ∪ C
2. At a newsstand, out of 46 customers, 27 bought the Daily News, 18 bought the Tribune, and 6 bought both papers. Use a Venn diagram to answer the following questions:
How many customers bought only one paper?
How many customers bought something other than either of the two papers?
3. State whether each pair of sets is equal, equivalent, or neither.
{d,o,g}: {c,a,t}
{run} : {{r,u,n}
{t,o,p} :{p,o,t}
{10,20,30} : {1,3,5}
Paper must be written in 3rd person.
Your paper should be about 4-5 pages in length or longer (counting the title page and references page) and cite and integrate at least one credible outside source. The CSU-Global Library(Links to an external site.)Links to an external site. (Links to an external site.) is a great place to find resources. Your textbook is a credible resource.
Include a title page, introduction, body, conclusion, and a reference page.
The introduction should describe or summarize the topic or problem. It might discuss the importance of the topic or how it affects you or society as a whole, or it might discuss or describe the unique terminology associated with the topic.
The body of your paper should answer the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment.
The conclusion should summarize your thoughts about what you have determined from the data and your analysis, often with a broader personal or societal perspective in mind. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs.
Include any tables of data or calculations, calculated values, and/or graphs associated with this problem in the body of your assignment.

Essay Sample Content Preview:

Math Week 1 Critical Thinking
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Introduction
The union and intersection of sets are some of the most used operations, in relation to set theory. A set is simply a grouping of two or more elements that are clearly distinguishable from each other. Based on the sets combining the elements helps to solve some problematic situations that would otherwise be really complex without understanding how unions and interaction of sets operate. Joining two or more sets results in union of sets and the Venn diagrams are useful to depict the relationships between elements in different sets (Tussy & Gustafson, 2013). In the case of intersection of sets only the elements the sets have in common are part of the new set. The union and intersection of sets are used to solve the problems including the case of the newsstand, while there is focus on the equal and equivalent sets.
Union and intersection of sets
When expressing the union of sets using the Venn diagrams, there is a need to first represent all the elements in their respective sets and then include all without repeating them in the same diagram (Aufmann & Lockwood, 2014). There are zones in the diagram and where there are only elements of A, another where there are only elements of B, and elements of C and other zones a third where there are elements in either two and a zone where the three intersect and there are no common elements.
A = {l, m, n, o, p}, B = {o, p, q, r}, and C = {r, s, t, u}(A ∪ B) ∩ C(A ∪ B) = {l, m ,n, o, p, q, r} ∩ {r, s, t, u} and (A ∪ B) ∩ C= {r}
The union of set A and set B results in the elements {l, m ,n, o, p, q, r} since the new set includes all the elements in both sets, and while o and p appear in both sets they are only included once. Now considering the intersection of the new set and set C it is only element r, which is common in both sets, and this is the final answer and shown in the Venn diagram. A ∩ (C ∪ B){l, m, n, o , p} ∩ {o, p, q, r, s, t, u}= {o, p}
First considering the union o of set C and set B the elements included in the new set are {o, p, q, r, s, t, u} where “r” is common in both sets and only included once. Thus, the problem involves solving set A and intersection with the new set {l, m, n, o, p} ∩ {o, p, q, r, s, t, u} is {o, p) since these are the only two common elements in both sets. Set C does not contain elements o and p and the solution is the same as the intersection of set A and set B.
(A ∩ B) ∪ C {l, m, n, o, p} ∩ {o, p, q, r} ∪ {r, s, t, u} {o, p} ∪ {r, s, t, u} = {o, p, r, s, t, u}
All the elements in their respective sets are represented first in the Venn diagram where elements o and p represent the common elements between set A and set B. Set A intersection set B is {o, p} since these are the only elements in set {l, m, n, o, p} and set {o, p, q, r}. The union of the new set {o, p} and {r, s, t, u} is {o, p, r, s, t, u}
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