1. Problem: Given the set $A = \{ 5, \{6, 7\}, 8 \}$, determine which of the following statements are true: (Choice A) $\{6, 7\} \subset A$ (Choice B) $\{5, 8\} \subset A$ (Choice C) $\{\{6, 7\}\} \subset A$ (Choice D) $7 \in A$ 2. Understand the set $A$: It contains three elements: the number 5, the set $\{6,7\}$, and the number 8. 3. Evaluate (Choice A): $\{6,7\} \subset A$ means every element of $\{6,7\}$ is in $A$. The elements 6 and 7 are inside a subset of $A$, but not directly elements of $A$. So (A) is false. 4. Evaluate (Choice B): $\{5,8\} \subset A$ means 5 and 8 are elements of $A$, which is true because 5 and 8 are directly in $A$. So (B) is true. 5. Evaluate (Choice C): $\{\{6,7\}\} \subset A$ means the set containing $\{6,7\}$ is a subset of $A$, i.e. $\{6,7\}$ itself is an element of $A$. Since $\{6,7\} \in A$, this makes $\{\{6,7\}\} \subset A$ true. 6. Evaluate (Choice D): $7 \in A$ means 7 itself is an element of $A$, which it is not because 7 is inside a subset of $A$, not directly in $A$. So (D) is false. 7. Final answers: (B) and (C) are true; (A) and (D) are false.