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CSS Pure Mathematics QUESTION #1257
Question 1
If \(\varphi: G \to H\) is an epimorphism (surjective homomorphism) with \(K = \ker\varphi\), then by the First Isomorphism Theorem:
  • G is isomorphic to H
  • \(G/K \cong H\)✔️
  • \(K \cong H\)
  • \(G \cong K \times H\)
Correct Answer Explanation
\(\textbf{First Isomorphism Theorem:}\) If \(\varphi: G\to H\) is an epimorphism, then \(G / \ker\varphi \cong H\). The quotient group \(G/K\) is isomorphic to the image \(H\).