Answer the following questions about the given sets. Are the sets equivalent? Explain. a. b. Are the sets equal? Explain. A={7, 7, 7, 8, 8, 9, 10, 11) B={11, 10, 9, 8, 7) a. Are the sets equivalent? Explain. O A. The sets are equivalent because n(A) = n(B). OB. The sets are not equivalent because n(A) = n(B). OC. The sets are equivalent because set A does not contain the exact same elements as set B. OD. The sets are not equivalent because set A does not contain the exact same elements as set B. b. Are the sets equal? Explain. O A. The sets are not equal because set A contains the exact same elements as set B. OB. The sets are not equal because n(A) = n(B). OC. The sets are equal because set A contains the exact same elements as set B. O D. The sets are equal because n(A) = n(B).
Answer the following questions about the given sets. Are the sets equivalent? Explain. a. b. Are the sets equal? Explain. A={7, 7, 7, 8, 8, 9, 10, 11) B={11, 10, 9, 8, 7) a. Are the sets equivalent? Explain. O A. The sets are equivalent because n(A) = n(B). OB. The sets are not equivalent because n(A) = n(B). OC. The sets are equivalent because set A does not contain the exact same elements as set B. OD. The sets are not equivalent because set A does not contain the exact same elements as set B. b. Are the sets equal? Explain. O A. The sets are not equal because set A contains the exact same elements as set B. OB. The sets are not equal because n(A) = n(B). OC. The sets are equal because set A contains the exact same elements as set B. O D. The sets are equal because n(A) = n(B).
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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Transcribed Image Text:### Understanding Sets: Equivalence and Equality
#### Problem Statement:
Answer the following questions about the given sets.
a. Are the sets equivalent? Explain.
b. Are the sets equal? Explain.
Given Sets:
A = {7, 7, 7, 8, 8, 9, 10, 11}
B = {11, 10, 9, 8, 7}
#### Questions and Multiple Choice Answers:
**a. Are the sets equivalent? Explain.**
- **A.** The sets are equivalent because n(A) = n(B).
- **B.** The sets are not equivalent because n(A) ≠ n(B).
- **C.** The sets are equivalent because set A does not contain the exact same elements as set B.
- **D.** The sets are not equivalent because set A does not contain the exact same elements as set B.
**b. Are the sets equal? Explain.**
- **A.** The sets are not equal because set A contains the exact same elements as set B.
- **B.** The sets are not equal because n(A) ≠ n(B).
- **C.** The sets are equal because set A contains the exact same elements as set B.
- **D.** The sets are equal because n(A) = n(B).
### Explanation:
**Equivalence of Sets:**
Equivalence of sets refers to whether two sets contain the same number of elements. Here:
- **Set A:** {7, 7, 7, 8, 8, 9, 10, 11}, which actually simplifies to {7, 8, 9, 10, 11} because sets are collections of distinct elements.
- **Set B:** {11, 10, 9, 8, 7}
Count of distinct elements:
- n(A) = 5 (after removing duplicates)
- n(B) = 5
So, the correct answer is:
- **A.** The sets are equivalent because n(A) = n(B).
**Equality of Sets:**
Equality of sets means that both sets contain exactly the same elements, regardless of order or repetition:
- Simplified Set A = {7, 8, 9, 10, 11}
- Simplified Set B = {11, 10, 9, 8, 7}
Both sets,
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