Home › MCQs › SSC Pure Mathematics › Question #11215
Back to Questions
SSC Pure Mathematics QUESTION #11215
Question 1
Let $\varphi: \mathbb{Z}\to\mathbb{Z}_5$ be $\varphi(a) = a\pmod{5}$. Then $\ker(\varphi) =$
  • $\{0\}$
  • $\{0,\pm5,\pm10,\ldots\}$✔️
  • $\mathbb{Z}_5$
  • $\mathbb{Z}$
Correct Answer Explanation
$\ker(\varphi) = \{a\in\mathbb{Z}: \varphi(a) = 0\} = \{a\in\mathbb{Z}: a\equiv 0\pmod{5}\} = \{\ldots,-10,-5,0,5,10,\ldots\} = 5\mathbb{Z} = \{0,\pm5,\pm10,\ldots\}$.