For each pair of statements, choose the one that is true. (a) \( 5 \subseteq\{4,5,6\} \) \( 5 \notin\{4,6,7\} \) (b) \( \{9,11,13\} \in\{1,3,5,7, \ldots\} \) \( \{9,11,13\} \subseteq\{1,3,5,7, \ldots\} \) (c) \( \{m\} \in\{m, r\} \) \( m \in\{m, r\} \) \( \{h\} \subseteq\{h, k\} \) (d) \( h \subseteq\{h, k\} \)

Let's analyze each pair of statements one by one to determine which one is true. ### (a) 1. **Statement 1:** \( 5 \subseteq \{4,5,6\} \) This statement is false because \( 5 \) is not a set; it is an element. The subset relation applies to sets, not individual elements. 2. **Statement 2:** \( 5 \notin \{4,6,7\} \) This statement is true because \( 5 \) is not an element of the set \( \{4,6,7\} \). **Conclusion for (a):** The true statement is \( 5 \notin \{4,6,7\} \). ### (b) 1. **Statement 1:** \( \{9,11,13\} \in \{1,3,5,7, \ldots\} \) This statement is false because \( \{9,11,13\} \) is a set, and the set \( \{1,3,5,7, \ldots\} \) contains only individual elements, not sets. 2. **Statement 2:** \( \{9,11,13\} \subseteq \{1,3,5,7, \ldots\} \) This statement is also false because none of the elements \( 9, 11, 13 \) are in the set \( \{1,3,5,7, \ldots\} \). **Conclusion for (b):** Both statements are false. ### (c) 1. **Statement 1:** \( \{m\} \in \{m, r\} \) This statement is false because \( \{m\} \) is a set containing \( m \), and the set \( \{m, r\} \) contains the elements \( m \) and \( r \), not the set \( \{m\} \). 2. **Statement 2:** \( m \in \{m, r\} \) This statement is true because \( m \) is indeed an element of the set \( \{m, r\} \). 3. **Statement 3:** \( \{h\} \subseteq \{h, k\} \) This statement is true because the set \( \{h\} \) is a subset of the set \( \{h, k\} \). **Conclusion for (c):** The true statements are \( m \in \{m, r\} \) and \( \{h\} \subseteq \{h, k\} \). ### (d) 1. **Statement:** \( h \subseteq \{h, k\} \) This statement is false because \( h \) is an individual element, and the subset relation applies to sets. The correct statement would be \( \{h\} \subseteq \{h, k\} \). **Conclusion for (d):** The statement is false. ### Summary of True Statements: - (a): \( 5 \notin \{4,6,7\} \) - (b): Both statements are false. - (c): \( m \in \{m, r\} \) and \( \{h\} \subseteq \{h, k\} \) are true. - (d): False. Thus, the true statements are: - From (a): \( 5 \notin \{4,6,7\} \) - From (c): \( m \in \{m, r\} \) and \( \{h\} \subseteq \{h, k\} \) are true.