Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**Question:**
Use the union rule to answer the question.
If \( n(A) = 10 \), \( n(B) = 11 \), and \( n(A \cap B) = 7 \), what is \( n(A \cup B) \)?
\[ n(A \cup B) = \, \_\_\_\_ \, \text{(Type a whole number.)} \]
**Explanation:**
To find the number of elements in the union of two sets \( A \) and \( B \), use the formula for the union of two sets:
\[
n(A \cup B) = n(A) + n(B) - n(A \cap B)
\]
Plugging in the given values:
\[
n(A \cup B) = 10 + 11 - 7
\]
\[
n(A \cup B) = 21 - 7
\]
\[
n(A \cup B) = 14
\]
So, the number of elements in the union of sets \( A \) and \( B \) is 14.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16622cdc-84cb-4ec0-9d95-93d27d44a93d%2Fb5889e87-88d4-465b-bead-292610b61d63%2Fvpu7woi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Use the union rule to answer the question.
If \( n(A) = 10 \), \( n(B) = 11 \), and \( n(A \cap B) = 7 \), what is \( n(A \cup B) \)?
\[ n(A \cup B) = \, \_\_\_\_ \, \text{(Type a whole number.)} \]
**Explanation:**
To find the number of elements in the union of two sets \( A \) and \( B \), use the formula for the union of two sets:
\[
n(A \cup B) = n(A) + n(B) - n(A \cap B)
\]
Plugging in the given values:
\[
n(A \cup B) = 10 + 11 - 7
\]
\[
n(A \cup B) = 21 - 7
\]
\[
n(A \cup B) = 14
\]
So, the number of elements in the union of sets \( A \) and \( B \) is 14.
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