1. **Problem:** Given set $A = \{2,3,5,7,11,13,17,19,23\}$, complete with $\in$, $\subset$, $\not\subset$, or $\supset$: a. $9 \;\_\_\_\_ A$ b. $3 \;\_\_\_\_ \{\text{prime numbers}\}$ c. $\{1,2,7\} \;\_\_\_\_ A$ 2. **Formula and rules:** - $x \in A$ means $x$ is an element of set $A$. - $B \subset A$ means $B$ is a proper subset of $A$ (all elements of $B$ are in $A$, but $B \neq A$). - $B \not\subset A$ means $B$ is not a subset of $A$. - $A \supset B$ means $A$ is a superset of $B$. 3. **Step-by-step:** a. Is $9$ an element of $A$? No, because $9$ is not in the list of elements of $A$. So $9 \notin A$. b. Is $3$ an element of the set of prime numbers? Yes, $3$ is prime, so $3 \in \{\text{prime numbers}\}$. c. Is $\{1,2,7\}$ a subset of $A$? Check if all elements are in $A$: - $1$ is not in $A$. - $2$ and $7$ are in $A$. Since $1 \notin A$, $\{1,2,7\} \not\subset A$. **Final answers:** - a. $9 \notin A$ - b. $3 \in \{\text{prime numbers}\}$ - c. $\{1,2,7\} \not\subset A$