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)

Answered: A All B (ii), (iii) D E None (i), (iii)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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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.