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Chapter 2: Problem 146

Describe the Venn diagram for two sets with common elements. How does the diagram illustrate this relationship?

Short Answer

Expert verified
In a Venn diagram, two sets with common elements are represented by overlapping circles. The area of overlap, called intersection, represents the common elements in both the sets.

Step by step solution

01

Title

Understand the concept of sets and Venn diagrams. Sets are collections of distinct objects, referred to as elements of the set. A Venn diagram is a diagrammatic representation of sets. It uses circles or other shapes to represent sets with each shape representing a set.
02

Title

Illustrate two sets with common elements using a Venn diagram. On a sheet of paper (or a board), draw two overlapping circles. Each circle represents a set. Label them as 'Set A' and 'Set B'. The overlapping area represents the common elements between the two sets. This area is known as 'Intersection of Set A and Set B' or simply 'A 鈭� B'.
03

Title

Explain how the Venn Diagram illustrates the relationship between two sets with common elements. The two circles signify two sets, the area where the circles overlap signifies the common elements present in both sets A and B. This illustrates intersection of two sets.

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Most popular questions from this chapter

Let $$ \begin{aligned} U &=\\{1,2,3,4,5,6,7\\} \\ A &=\\{1,3,5,7\\} \\ B &=\\{1,2,3\\} \\ C &=\\{2,3,4,5,6\\} \end{aligned} $$ Find each of the following sets. \((A \cap B) \cup(A \cap C)\)

A pollster conducting a telephone poll of a city's residents asked two questions: 1\. Do you currently smoke cigarettes? 2\. Regardless of your answer to question 1, would you support a ban on smoking in all city parks? a. Construct a Venn diagram that allows the respondents to the poll to be identified by whether or not they smoke cigarettes and whether or not they support the ban. b. Write the letter b in every region of the diagram that represents smokers polled who support the ban. c. Write the letter \(\mathrm{c}\) in every region of the diagram that represents nonsmokers polled who support the ban. d. Write the letter d in every region of the diagram that represents nonsmokers polled who do not support the ban.

Describe the Venn diagram for two equal sets. How does this diagram illustrate that the sets are equal?

In Exercises 97-104, let $$ \begin{aligned} U &=\\{x \mid x \in \mathbf{N} \text { and } x<9\\} \\ A &=\\{x \mid x \text { is an odd natural number and } x<9\\} \\ B &=\\{x \mid x \text { is an even natural number and } x<9\\} \\ C &=\\{x \mid x \in \mathbf{N} \text { and } 1

Make Sense? Determine whether each statement makes sense or does not make sense, and explain your reasoning. Even if I'm not sure how mathematicians define irrational and complex numbers, telling me how these sets are related, I can construct a Venn diagram illustrating their relationship.
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