Yes, $\{2\} \subseteq \{1, \{2\}, \{3\}\}$.

Explanation:

For $\{2\} \subseteq \{1, \{2\}, \{3\}\}$ to be true, every element of the set $\{2\}$ must be an element of the set $\{1, \{2\}, \{3\}\}$.

• The only element in $\{2\}$ is $2$.
• The set $\{1, \{2\}, \{3\}\}$ contains the element $\{2\}$, but not the element $2$ itself. Thus, $\{2\}$ is not a subset of $\{1, \{2\}, \{3\}\}$.

So the correct answer is no.

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5 Related Questions:

1. What is the difference between a set and an element of a set?
2. How do you determine if a set is a subset of another set?
3. What does it mean for a set to be a proper subset?
4. What is the difference between $\subseteq$ and $\in$?
5. How can you prove whether one set is a subset of another?

Tip:

Always remember that for $\{a\} \subseteq \{b\}$ to be true, $a$ must be an element of $\{b\}$. A set $\{a\}$ does not necessarily mean that $a$ is an element of the other set directly—it's the elements of the sets that matter.