Let's analyze each statement carefully. Statement 1: "A factor group of a non-Abelian group is non-Abelian." **Analysis:** - A factor group (or quotient group) is formed by partitioning a group \( G \) by a normal subgroup \( N \), denoted \( G/N \). - A group is non-Abelian if there exist elements \( a \) and \( b \) in the group such that \( ab \neq ba \). - It is possible to create a factor group from a non-Abelian group that is Abelian. For example, consider the symmetric group \( S_3 \), which is non-Abelian. If we take the normal subgroup generated by a transposition (say, \( (1 2) \)), the quotient group \( S_3/\langle (1 2) \rangle \) can be shown to be Abelian (specifically, isomorphic to \( S_3 \) mod the subgroup generated by \( (1 2) \)). - Therefore, it is not necessarily true that a factor group of a non-Abelian group is non-Abelian. **Conclusion for Statement 1:** False. Statement 2: "If \( K \) is a normal subgroup of \( H \) and \( H \) is a normal subgroup of \( G \), then \( K \) is a normal subgroup of \( G \)." **Analysis:** - By definition, \( K \) being a normal subgroup of \( H \) means that for every \( h \in H \) and \( k \in K \), the element \( hkh^{-1} \) is in \( K \). - Similarly, \( H \) being a normal subgroup of \( G \) means that for every \( g \in G \) and \( h \in H \), \( ghg^{-1} \) is in \( H \). - To show that \( K \) is normal in \( G \), we need to prove that for every \( g \in G \) and \( k \in K \), the element \( gkg^{-1} \) is in \( K \). - Since \( g \) is in \( G \), it acts on \( H \). Thus, for some \( h \in H \), \( g \in G \) implies that \( ghg^{-1} \in H \). - Additionally, since \( K \) is a normal subgroup of \( H \), we have \( hkh^{-1} \in K \) for all \( h \in H \). - If we take \( g \in G \) and apply it to \( K \), we can express \( gkg^{-1} \) as \( g(hkh^{-1})h^{-1} \) for some \( h \in H \) which will keep \( gkg^{-1} \) in \( K \), proving that \( K \) is indeed normal in \( G \). **Conclusion for Statement 2:** True. Final evaluation: - Statement 1 is **False**. - Statement 2 is **True**. Given the options: - (A) True, True - (B) True, False - (C) False, True

随着旅游业的快速发展，越来越多的人选择外出旅行。然而，选择一个好的旅游景区对于游客来说至关重要。旅游景区质量等级的划分与评定可以提供游客参考，帮助他们选择适合自己需求的景区，从而避免可能发生的不良体验。

旅游景区质量等级划分的标准

旅游景区质量等级的划分不仅包括景区的景观、服务质量，还包括安全设施、卫生条件等方面。景区管理部门会根据景区的设施设备、景观独特性、服务水平等多个指标进行评定，最终给出相应的质量等级。

评定的重要性

旅游景区质量等级的评定对于景区经营者来说同样重要。一个高质量的景区可以吸引更多游客，提高经济效益。同时，景区管理者也可以根据评定结果发现自身存在的问题并进行改进，提升整体运营水平。

实施策略探讨

为了确保旅游景区质量等级划分与评定的公正性和客观性，需要建立健全的评定标准和程序。同时，相关部门需要加强对景区的监督管理，保障各项指标的执行情况。此外，景区可以通过提升服务质量、加强安全防范等措施来提高自身的质量等级。

结语

旅游景区质量等级划分与评定对游客和景区经营者都具有重要意义。只有通过科学的评定体系，才能确保游客的权益得到充分保障，同时也能帮助景区提升自身的管理水平和服务质量。希望在未来的发展中，旅游景区的质量等级能够得到更加完善和规范的评定。