3) Suppose Set A contains 60 elements and Set B contains 59 elements. If the total number elements in either Set A or Set B is 89, how many elements do Sets A and B have in common?
3) Suppose Set A contains 60 elements and Set B contains 59 elements. If the total number elements in either Set A or Set B is 89, how many elements do Sets A and B have in common?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem 3**
Suppose Set A contains 60 elements and Set B contains 59 elements. If the total number of elements in either Set A or Set B is 89, how many elements do Sets A and B have in common?
**Explanation:**
To find how many elements Sets A and B have in common, we use the formula for the union of two sets:
\[ |A \cup B| = |A| + |B| - |A \cap B| \]
Where:
- \( |A \cup B| \) is the number of elements in either Set A or Set B,
- \( |A| \) is the number of elements in Set A,
- \( |B| \) is the number of elements in Set B,
- \( |A \cap B| \) is the number of elements common to both sets.
Substituting the given values:
\[ 89 = 60 + 59 - |A \cap B| \]
Solving for \( |A \cap B| \):
\[ |A \cap B| = 60 + 59 - 89 \]
\[ |A \cap B| = 119 - 89 \]
\[ |A \cap B| = 30 \]
Thus, Sets A and B have 30 elements in common.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a52f50e-f337-471a-921b-d2b360c21876%2Ff7403412-9e6d-4546-8f84-97a8338c41de%2Fmi4k22q_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 3**
Suppose Set A contains 60 elements and Set B contains 59 elements. If the total number of elements in either Set A or Set B is 89, how many elements do Sets A and B have in common?
**Explanation:**
To find how many elements Sets A and B have in common, we use the formula for the union of two sets:
\[ |A \cup B| = |A| + |B| - |A \cap B| \]
Where:
- \( |A \cup B| \) is the number of elements in either Set A or Set B,
- \( |A| \) is the number of elements in Set A,
- \( |B| \) is the number of elements in Set B,
- \( |A \cap B| \) is the number of elements common to both sets.
Substituting the given values:
\[ 89 = 60 + 59 - |A \cap B| \]
Solving for \( |A \cap B| \):
\[ |A \cap B| = 60 + 59 - 89 \]
\[ |A \cap B| = 119 - 89 \]
\[ |A \cap B| = 30 \]
Thus, Sets A and B have 30 elements in common.
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