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5. (8 points) Let \( S_4 \) be the set of all strings of 0's and 1's of length 4. Define \( F: S_4 \to \mathbb{Z}_{\text{nonneg}} \) such that \( F(s) \) = Number of zeros in \( s \), for any \( s \in S_4 \) a) Find \( F(1000) \) b) What is the range of \( F \)? EXPLAIN. c) Explain why \( F \) is not onto. d) Explain why \( F \) is not one-to-one.

5. (8 points) Let \( S_4 \) be the set of all strings of 0's and 1's of length 4. Define \( F: S_4 \to \mathbb{Z}_{\text{nonneg}} \) such that \( F(s) \) = Number of zeros in \( s \), for any \( s \in S_4 \) a) Find \( F(1000) \) b) What is the range of \( F \)? EXPLAIN. c) Explain why \( F \) is not onto. d) Explain why \( F \) is not one-to-one.

Advanced Engineering Mathematics
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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5. (8 points) Let \( S_4 \) be the set of all strings of 0's and 1's of length 4. Define \( F: S_4 \to \mathbb{Z}_{\text{nonneg}} \) such that \( F(s) \) = Number of zeros in \( s \), for any \( s \in S_4 \) a) Find \( F(1000) \) b) What is the range of \( F \)? EXPLAIN. c) Explain why \( F \) is not onto. d) Explain why \( F \) is not one-to-one.
Transcribed Image Text:5. (8 points) Let \( S_4 \) be the set of all strings of 0's and 1's of length 4. Define \( F: S_4 \to \mathbb{Z}_{\text{nonneg}} \) such that \( F(s) \) = Number of zeros in \( s \), for any \( s \in S_4 \) a) Find \( F(1000) \) b) What is the range of \( F \)? EXPLAIN. c) Explain why \( F \) is not onto. d) Explain why \( F \) is not one-to-one.
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