Let $p$ and $q$ represent the following statements. \[ \begin{array}{l} \text { p: } 6+3=9 \\ \text { q: } 3 \times 7=42 \end{array} \] Determine the truth value for the statement $\sim p \wedge q$. Choose the correct truth value below. $\sim p \wedge q$ is false. $\sim p \wedge q$ is true.

Step 1 ：Let $p$ and $q$ represent the following statements.

Step 2 ：$p: 6 + 3 = 9$

Step 3 ：$q: 3 \times 7 = 42$

Step 4 ：Determine the truth value for the statement $\sim p \wedge q$.

Step 5 ：The statement $\sim p \wedge q$ is a logical conjunction of the negation of statement $p$ and statement $q$.

Step 6 ：To determine the truth value of this statement, we first need to determine the truth values of $p$ and $q$.

Step 7 ：Statement $p$ is '$6 + 3 = 9$', which is true. Therefore, the negation of $p$, denoted as $\sim p$, is false.

Step 8 ：Statement $q$ is '$3 \times 7 = 42$', which is false.

Step 9 ：The logical conjunction of two statements is true if and only if both statements are true.

Step 10 ：Since $\sim p$ is false and $q$ is false, the statement $\sim p \wedge q$ is false.

Step 11 ：Final Answer: $\sim p \wedge q$ is \(\boxed{\text{false}}\).