1. **State the problem:** Determine which of the given sets are subsets of the set $$A = \{1, \{2, 3, 4\}, \{5, \{6\}\}, 7, 8\}$$. 2. **Recall the definition of subset:** A set $$B$$ is a subset of $$A$$, written $$B \subseteq A$$, if every element of $$B$$ is also an element of $$A$$. 3. **Analyze each candidate subset:** - $$\emptyset \subseteq A$$: The empty set is a subset of every set by definition. - $$\{2, 3, 4\} \subseteq A$$: Check if each element 2, 3, and 4 is in $$A$$. They are not elements of $$A$$ directly; instead, $$\{2, 3, 4\}$$ is an element of $$A$$, but its individual elements are not. - $$\{1, 7, 8\} \subseteq A$$: Elements 1, 7, and 8 are all in $$A$$. - $$\{\{2, 3, 4\}\} \subseteq A$$: The set $$\{2, 3, 4\}$$ is an element of $$A$$, so this singleton set is a subset. - $$\{5, \{6\}\} \subseteq A$$: Check if 5 and $$\{6\}$$ are elements of $$A$$. 5 is not an element of $$A$$, but $$\{5, \{6\}\}$$ is an element of $$A$$. So this set is not a subset. - $$\{\{5, \{6\}\}, 7, 8\} \subseteq A$$: Elements $$\{5, \{6\}\}$$, 7, and 8 are all elements of $$A$$. 4. **Final answers:** - $$\emptyset \subseteq A$$: True - $$\{2, 3, 4\} \subseteq A$$: False - $$\{1, 7, 8\} \subseteq A$$: True - $$\{\{2, 3, 4\}\} \subseteq A$$: True - $$\{5, \{6\}\} \subseteq A$$: False - $$\{\{5, \{6\}\}, 7, 8\} \subseteq A$$: True