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

Question

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 · Accepted Answer

To determine how the student is misunderstanding the word "or" in the definition of set union, we need to analyze the given sets $$ A $$ and $$ B $$ and the student's answer.

Given:
$$ A = \{a, b, c, d\} $$
$$ B = \{c, d, e, f, g, h\} $$
Student's answer: $$ \{a, b, e, f, g, h\} $$

The student's answer includes elements from both sets $$ A $$ and $$ B $$, but it does not include the common elements $$ c $$ and $$ d $$ 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 $$ A $$ or set $$ B $$, or both. Therefore, the student's answer is incorrect because it does not include the common elements $$ c $$ and $$ d $$.

Let's calculate the correct union of sets $$ A $$ and $$ B $$ to verify the student's answer.

The union of sets $$ A $$ and $$ B $$ is given by:
$$ A \cup B = \{a, b, c, d, e, f, g, h\} $$

Therefore, the correct answer is:
B. The student interpreted "or" as "and" in which both possibilities hold.
The student misunderstood "or" as "and," thinking that both sets must be included together, which excluded the common elements $$ c $$ and $$ d $$.

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Other Questions