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A student is told that AUB is the set of all elements that belong to or to . However, when asked to find the union of and , the student says
that the answer is . How is the word “or” in the definition of set union being misunderstood? Give an everyday example where “or” is used in the
mathematical sense.
Choose the correct answer below. Use the Show Work feature to provide related calculations and additional reasoning to support your answer.
A. The student interpreted AUB as AnB, and listed the correct set of elements in AnB.
B. The student interpreted “or” as “and” in which both possibilities hold.
C. The student interpreted AUB as BUA, and listed the correct set of elements in BUA.
D. The student interpreted “or” as the “exclusive or” in which either one of two possibilities holds, but not both.

Ask by Chadwick Turner. in the United States
Mar 17,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The student misunderstood “or” as “and,” thinking that both sets must be included together, which excluded the common elements and .

Solution

To determine how the student is misunderstanding the word “or” in the definition of set union, we need to analyze the given sets and and the student’s answer.
Given:


Student’s answer:
The student’s answer includes elements from both sets and , but it does not include the common elements and that are present in both sets. This indicates that the student is misunderstanding the word “or” in the definition of set union.
The correct interpretation of “or” in the definition of set union is that it includes all elements that belong to either set or set , or both. Therefore, the student’s answer is incorrect because it does not include the common elements and .
Let’s calculate the correct union of sets and to verify the student’s answer.
The union of sets and is given by:
Therefore, the correct answer is:
B. The student interpreted “or” as “and” in which both possibilities hold.

Answered by UpStudy AI and reviewed by a Professional Tutor

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Simplify this solution

Beyond the Answer

The misunderstanding stems from the interpretation of “or.” The student mistakenly viewed “or” as “exclusive or,” meaning they thought that the elements could either belong to set or set , but not both at the same time. In this case, they excluded the common elements and from the union. In everyday language, “or” is often used in a way that implies one choice but not both, such as when someone says, “You can have tea or coffee,” suggesting you must choose one but not both.
To clarify the correct interpretation, the union should include all elements from both sets, leading to the correct result of .
So, the right answer is:
D. The student interpreted “or” as the “exclusive or” in which either one of two possibilities holds, but not both.

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