Reading Section 2.3 Problems Consider f : A → B and let S,T C A. 1. Prove: f(SnT) C f(S) n f(T) 2. Draw a diagram that shows why this is a subset relationship and not set equality. In other words, show why there can be elements in f(S) n f(T) that are not in f(SnT). 3. How can f be limited so that equality occurs. In other words, how do you eliminate the problem in your drawing? 4. Which step in your proof is not reversible?
Reading Section 2.3 Problems Consider f : A → B and let S,T C A. 1. Prove: f(SnT) C f(S) n f(T) 2. Draw a diagram that shows why this is a subset relationship and not set equality. In other words, show why there can be elements in f(S) n f(T) that are not in f(SnT). 3. How can f be limited so that equality occurs. In other words, how do you eliminate the problem in your drawing? 4. Which step in your proof is not reversible?
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:Reading
Section 2.3
Problems
Consider f : A → B and let S,T C A.
1. Prove: f(SnT) C f(S) n f(T)
2. Draw a diagram that shows why this is a subset relationship and not set equality. In other
words, show why there can be elements in f(S) n f(T) that are not in f(SnT).
3. How can f be limited so that equality occurs. In other words, how do you eliminate the
problem in your drawing?
4. Which step in your proof is not reversible?
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