1. **State the problem:** We are given the set $$B = \{1, \{2, 3\}, 4, \{5, \{6, 7\}\}, 8\}$$ and asked to determine which of the listed elements are members of set $$B$$. 2. **Recall the definition of set membership:** An element $$x$$ is a member of a set $$S$$ if $$x$$ appears directly inside the curly braces of $$S$$. 3. **Analyze the elements of $$B$$:** The elements of $$B$$ are: - $$1$$ - $$\{2, 3\}$$ (a set containing 2 and 3) - $$4$$ - $$\{5, \{6, 7\}\}$$ (a set containing 5 and another set $$\{6, 7\}$$) - $$8$$ 4. **Check each candidate:** - $$1$$ is directly in $$B$$, so yes. - $$2$$ is inside $$\{2, 3\}$$ which is an element of $$B$$, but $$2$$ itself is not directly in $$B$$, so no. - $$3$$ same reasoning as $$2$$, no. - $$4$$ is directly in $$B$$, yes. - $$5$$ is inside $$\{5, \{6, 7\}\}$$ which is in $$B$$, so no. - $$6$$ is inside $$\{6, 7\}$$ which is inside $$\{5, \{6, 7\}\}$$ which is in $$B$$, so no. - $$7$$ same as $$6$$, no. - $$8$$ is directly in $$B$$, yes. - $$\{\}$$ (empty set) is not listed as an element, no. - $$\{2, 3\}$$ is directly in $$B$$, yes. - $$\{6, 7\}$$ is inside $$\{5, \{6, 7\}\}$$ which is in $$B$$, but $$\{6, 7\}$$ itself is not directly in $$B$$, so no. - $$\{5, \{6, 7\}\}$$ is directly in $$B$$, yes. 5. **Final answer:** The elements of $$B$$ from the list are $$1, 4, 8, \{2, 3\}, \{5, \{6, 7\}\}$$.