1. **Problem statement:** Given the set $A = \{1, 2, 3\}$, classify each statement as true or false: $2 \in A$, $3 \subset A$, $\emptyset \in A$, $\{0\} \subset A$, $A \cup \{\emptyset\} = A$. 2. **Recall definitions:** - $x \in A$ means $x$ is an element of $A$. - $B \subset A$ means $B$ is a subset of $A$, i.e., every element of $B$ is in $A$. - $\emptyset$ is the empty set with no elements. - Union $A \cup B$ contains all elements in $A$ or $B$. 3. **Evaluate each statement:** - $2 \in A$: Since $2$ is listed in $A$, this is **true**. - $3 \subset A$: $3$ is an element, not a set, so it cannot be a subset. This is **false**. - $\emptyset \in A$: The empty set is not an element of $A$, so **false**. - $\{0\} \subset A$: $\{0\}$ contains $0$, which is not in $A$, so **false**. - $A \cup \{\emptyset\} = A$: $\{\emptyset\}$ adds the empty set as an element, which is not in $A$, so the union is $\{1,2,3,\emptyset\}$, not equal to $A$. So **false**. **Final answers:** - $2 \in A$: true - $3 \subset A$: false - $\emptyset \in A$: false - $\{0\} \subset A$: false - $A \cup \{\emptyset\} = A$: false