10. The Proof of Theorem 6.21. Use the ideas from Exercise (9) to prove The- orem 6.21. Let A, B, and C be nonempty sets and let f: A →B and g: B C. (a) If go f: A -→ C is an injection, then f: A → B is an injection. (b) If go f: A → C is a surjection, then g: B → C is a surjection. Hint: For part (a), start by asking, "What do we have to do to prove that f is an injection?" Start with a similar question for part (b).
10. The Proof of Theorem 6.21. Use the ideas from Exercise (9) to prove The- orem 6.21. Let A, B, and C be nonempty sets and let f: A →B and g: B C. (a) If go f: A -→ C is an injection, then f: A → B is an injection. (b) If go f: A → C is a surjection, then g: B → C is a surjection. Hint: For part (a), start by asking, "What do we have to do to prove that f is an injection?" Start with a similar question for part (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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I need help with b
Transcribed Image Text:or explain why it is not possible.
10. The Proof of Theorem 6.21. Use the ideas from Exercise (9) to prove The-
orem 6.21. Let A, B, and C be nonempty sets and let f: A B and
g: B C.
(a) If g o f: A -→ C is an injection, then f: A → B is an injection.
(b) If go f: A → C is a surjection, then g: B → C is a surjection.
Hint: For part (a), start by asking, "What do we have to do to prove that f
is an injection?" Start with a similar question for part (b).
SH
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