blems 1-10 refer to these sets: Find each of the following: U = (a, b, c, d, e.f} A (a,c, e, f) B = (c, d, e} C (e,f) 1. A' 6. BoC 2. B' 7. (AUB) 3. С" 8. A'UB' 4. BoC 9. B'nC 5. AnC 10. A (B'nC) heorem: If JA| = n then |P(A)| = 2" (Every set with n elements has 2" subsets.) %3D neorem: |AU B = 1A|+1B|-1A n BI (The Inclusion-Exclusion Principle) eorem: |A UBU CI 1A|+1B1 + 1CI-1An B1-1Ancl-IB C+1A NBNC
blems 1-10 refer to these sets: Find each of the following: U = (a, b, c, d, e.f} A (a,c, e, f) B = (c, d, e} C (e,f) 1. A' 6. BoC 2. B' 7. (AUB) 3. С" 8. A'UB' 4. BoC 9. B'nC 5. AnC 10. A (B'nC) heorem: If JA| = n then |P(A)| = 2" (Every set with n elements has 2" subsets.) %3D neorem: |AU B = 1A|+1B|-1A n BI (The Inclusion-Exclusion Principle) eorem: |A UBU CI 1A|+1B1 + 1CI-1An B1-1Ancl-IB C+1A NBNC
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Please read carefully and answer correctly as you can get a better understanding of these questions. Only answer if you can answer answer these 10 questions shown in the picture. This question deals with Sets and set operations with Venn Diagram.
For problems 1-10 refer to these sets
U= {a, b, c, d, e, f}
A= {a, c, e, f}
B={c, d, e}
C={e, f}
![For problems 1 - 10 refer to these sets:
\[ U = \{a, b, c, d, e, f\}, \quad A = \{a, c, e, f\}, \quad B = \{c, d, e\}, \quad C = \{e, f\} \]
**Find each of the following:**
1. \( A' \)
\_\_\_\_\_\_\_\_
2. \( B' \)
\_\_\_\_\_\_\_\_
3. \( C' \)
\_\_\_\_\_\_\_\_
4. \( B \cup C \)
\_\_\_\_\_\_\_\_
5. \( A \cap C \)
\_\_\_\_\_\_\_\_
6. \( B \cap C \)
\_\_\_\_\_\_\_\_
7. \( (A \cup B)' \)
\_\_\_\_\_\_\_\_
8. \( A' \cup B' \)
\_\_\_\_\_\_\_\_
9. \( B' \cap C \)
\_\_\_\_\_\_\_\_
10. \( A \cup (B' \cap C) \)
\_\_\_\_\_\_\_\_
**Theorems:**
- Theorem: If \(|A| = n\) then \(|P(A)| = 2^n\) [Every set with \(n\) elements has \(2^n\) subsets.]
- Theorem: \(|A \cup B| = |A| + |B| - |A \cap B|\) (The Inclusion-Exclusion Principle)
- Theorem:
\[
|A \cup B \cup C| = |A| + |B| + |C| - |A \cap B| - |A \cap C| - |B \cap C| + |A \cap B \cap C|
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fceea8825-7913-465d-b473-498b11b36f04%2Fde6a8e01-b8f4-4b0a-bd35-b8e0fff52931%2Fco3a8xs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For problems 1 - 10 refer to these sets:
\[ U = \{a, b, c, d, e, f\}, \quad A = \{a, c, e, f\}, \quad B = \{c, d, e\}, \quad C = \{e, f\} \]
**Find each of the following:**
1. \( A' \)
\_\_\_\_\_\_\_\_
2. \( B' \)
\_\_\_\_\_\_\_\_
3. \( C' \)
\_\_\_\_\_\_\_\_
4. \( B \cup C \)
\_\_\_\_\_\_\_\_
5. \( A \cap C \)
\_\_\_\_\_\_\_\_
6. \( B \cap C \)
\_\_\_\_\_\_\_\_
7. \( (A \cup B)' \)
\_\_\_\_\_\_\_\_
8. \( A' \cup B' \)
\_\_\_\_\_\_\_\_
9. \( B' \cap C \)
\_\_\_\_\_\_\_\_
10. \( A \cup (B' \cap C) \)
\_\_\_\_\_\_\_\_
**Theorems:**
- Theorem: If \(|A| = n\) then \(|P(A)| = 2^n\) [Every set with \(n\) elements has \(2^n\) subsets.]
- Theorem: \(|A \cup B| = |A| + |B| - |A \cap B|\) (The Inclusion-Exclusion Principle)
- Theorem:
\[
|A \cup B \cup C| = |A| + |B| + |C| - |A \cap B| - |A \cap C| - |B \cap C| + |A \cap B \cap C|
\]
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