MHB Set Problems: Is My Statement about Circles True?

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The discussion clarifies the distinction between subsets and elements in set theory. It confirms that the empty set, denoted as $\emptyset$, is a subset of every set, including $\{1, 2, 3\}$. However, $\emptyset$ is not an element of the set $\{1, 2, 3\}$. The participants agree on these definitions, reinforcing the understanding of set relationships. This highlights the importance of accurately interpreting set properties in mathematical statements.
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Is the statement that I have circle is true ?
Because I feel like the solution in my textbook is wrong, I only learn that empty set is a subset of every set but it is not an element of a set.
 
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You are right: $\emptyset$ is not an element of $\{1, 2, 3\}$. The only elements of that set are 1, 2 and 3.
 
Of course, the empty set, $\phi$, is a subset of every set so it is true that $\phi\subset \{1, 2, 3\}$.
 
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