/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 151 Describe how to find the cardina... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 151

Describe how to find the cardinal number of the union of two finite sets.

Short Answer

Expert verified
To find the cardinal number of the union of two finite sets, firstly calculate the cardinalities of the individual sets. Then, determine the intersection of the two sets and find its cardinality. Lastly, use the formula |A 鈭� B| = |A| + |B| - |A 鈭� B| to get the cardinal number of the union.

Step by step solution

01

Identify the sets

Identify the two finite sets A and B that are given in the problem. Determine the elements present in each of these sets.
02

Find the cardinalities

Calculate the cardinalities of the individual sets, |A| and |B|. The cardinality of a set is simply the number of elements in the set.
03

Determine the intersection

Find the intersection of the two sets, A 鈭� B, which are the elements that are shared between both sets.
04

Calculate the cardinality of the intersection

Calculate the number of elements in the intersection |A 鈭� B|, which is the cardinality of the intersection.
05

Determine union cardinality

With values |A|, |B|, and |A 鈭� B|, use the principle |A 鈭� B| = |A| + |B| - |A 鈭� B| to compute the cardinality of the union.

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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. \((A \cap B) \cup(A \cap C)\)

Construct a Venn diagram illustrating the given sets. \(\begin{aligned} A &=\left\\{x_{3}, x_{9}\right\\} \\ B &=\left\\{x_{1}, x_{2}, x_{3}, x_{5}, x_{6}\right\\} \\ C &=\left\\{x_{3}, x_{4}, x_{5}, x_{6}, x_{9}\right\\} \\ U &=\left\\{x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}, x_{7}, x_{8}, x_{9}\right\\} \end{aligned}\)

A survey of 120 college students was taken at registration. Of those surveyed, 75 students registered for a math course, 65 for an English course, and 40 for both math and English. Of those surveyed, a. How many registered only for a math course? b. How many registered only for an English course? c. How many registered for a math course or an English course? d. How many did not register for either a math course or an English course?

In Exercises 29-32, use the Venn diagram and the given conditions to determine the number of elements in each region, or explain why the conditions are impossible to meet. \(n(U)=38, n(A)=26, n(B)=21, n(C)=18\) \(n(A \cap B)=17, n(A \cap C)=11, n(B \cap C)=8\) \(n(A \cap B \cap C)=7\)

In Exercises 1-12, 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. \(A \cap(B \cup C)\)
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