1. **State the problem:** Given the set $$A = \{ \{-2, 2\}, \{-1, 1\}, 0 \}\), determine which of the following subset statements are true. 2. **Analyze Choice A:** $$\{ -2, 2 \} \subset A$$ means every element of $$\{ -2, 2 \}$$ is an element of $$A$$. - The elements of $$\{ -2, 2 \}$$ are $$-2$$ and $$2$$. - The elements of $$A$$ are $$\{-2,2\}$$, $$\{-1,1\}$$, and $$0$$. - Since $$-2$$ and $$2$$ are elements inside $$\{-2, 2\}$$ which is an element of $$A$$ but $$-2$$ and $$2$$ themselves are *not* direct elements of $$A$$, $$\{ -2, 2 \}$$ is *not* a subset of $$A$$. **Conclusion for A:** False. 3. **Analyze Choice B:** $$\{\{ -1, 1 \}\} \subset A$$ means the set whose single element is $$\{-1, 1\}$$ is a subset of $$A$$. - The element $$\{-1, 1\}$$ is indeed an element of $$A$$. - Therefore, every element of $$\{\{ -1, 1 \}\}$$ is in $$A$$. **Conclusion for B:** True. 4. **Analyze Choice C:** $$\{ \{0\} \} \subset A$$ means the singleton set containing the set $$\{0\}$$ is a subset of $$A$$. - The set $$\{0\}$$ is not an element of $$A$$ (the element is $$0$$ itself, not the set $$\{0\}$$). **Conclusion for C:** False. 5. **Analyze Choice D:** $$\{ -1, 0, 1 \} \subset A$$ means each of $$-1$$, $$0$$, and $$1$$ is an element of $$A$$. - Elements of $$A$$ are $$\{-2, 2\}$$, $$\{-1, 1\}$$, and $$0$$. - Neither $$-1$$ nor $$1$$ is an element of $$A$$; they are elements of $$\{-1,1\}$$ which is an element of $$A$$. **Conclusion for D:** False. **Final Answers:** Only Choice B is true.