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Chapter 2: Problem 81

In Exercises 81-90, a. Are the sets equivalent? Explain. b. Are the sets equal? Explain. \(A\) is the set of students at your college. \(B\) is the set of students majoring in business at your college.

Short Answer

Expert verified
Sets \(A\) and \(B\) are neither equivalent nor equal. This is because they do not contain the same number of elements (equivalent), nor do they have exactly the same elements (equal).

Step by step solution

01

Analyze Set \(A\)

Set \(A\) is defined as the set of all students at your college.
02

Analyze Set \(B\)

Set \(B\) consists of students majoring in business at your college. This means that every student in \(B\) is part of \(A\), but not every student in \(A\) is necessarily part of \(B\). This is important in understanding the next steps
03

Determine whether \(A\) and \(B\) are equivalent

As noted before, equivalent sets are those that have the same number of elements. In this case, unless all students are majoring in business, the size of Set \(A\) (all students) will be more than the size of Set \(B\) (business students). Therefore, \(A\) and \(B\) are not equivalent.
04

Determine whether \(A\) and \(B\) are equal

Again referring to the definition, equal sets are those with exactly the same elements. All elements in \(B\) are part of \(A\), but \(A\) certainly has other elements that \(B\) does not. Therefore, \(A\) and \(B\) are not equal.

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Most popular questions from this chapter

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