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A All B (ii), (iii) D E None (i), (iii) (i), (ii) Suppose such that (i): (ii): : Z→ Z40 is a group homomorphism and ker() = 20Z (12) = 8. Which of the following are true? (32) = 23. (-32) = 32. (iii): (52) = 8. (iv): p(-52) = 23.

A All B (ii), (iii) D E None (i), (iii) (i), (ii) Suppose such that (i): (ii): : Z→ Z40 is a group homomorphism and ker() = 20Z (12) = 8. Which of the following are true? (32) = 23. (-32) = 32. (iii): (52) = 8. (iv): p(-52) = 23.

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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Suppose \( \phi: \mathbb{Z} \rightarrow \mathbb{Z}_{40} \) is a group homomorphism and \( \ker(\phi) = 20 \mathbb{Z} \) such that \( \phi(12) = 8 \). Which of the following are true? (i): \( \phi(32) = 23 \). (ii): \( \phi(-32) = 32 \). (iii): \( \phi(52) = 8 \). (iv): \( \phi(-52) = 23 \). Options: - A: All - B: (ii), (iii) - C: None - D: (i), (iii) - E: (i), (ii)
Transcribed Image Text:Suppose \( \phi: \mathbb{Z} \rightarrow \mathbb{Z}_{40} \) is a group homomorphism and \( \ker(\phi) = 20 \mathbb{Z} \) such that \( \phi(12) = 8 \). Which of the following are true? (i): \( \phi(32) = 23 \). (ii): \( \phi(-32) = 32 \). (iii): \( \phi(52) = 8 \). (iv): \( \phi(-52) = 23 \). Options: - A: All - B: (ii), (iii) - C: None - D: (i), (iii) - E: (i), (ii)
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