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CSS Pure Mathematics QUESTION #1256
Question 1
Let \(N\) be a normal subgroup of \(G\) and \(H\) a subgroup of \(G\). Which of the following is a subgroup of \(G\)?
  • \(N \cap H\)
  • \(N \cup H\)
  • \(NH = \{nh : n\in N, h\in H\}\)
  • Both (A) and (C)✔️
Correct Answer Explanation
Both \(N\cap H\) (intersection of subgroups) and \(NH\) (product set when \(N\) is normal) are subgroups of \(G\). The union \(N\cup H\) is generally NOT a subgroup. Since the question asks which one from the listed options forms a subgroup, and option (D) correctly identifies both valid subgroup constructions, (D) is the complete answer.