Let $p$ and $q$ represent the following statements. \[ \begin{array}{l} p: 5+10=14 \\ q: 7 \times 3=42 \end{array} \] Determine the truth value for the statement $\sim p \vee \sim q$. Choose the correct truth value below. $\sim p \vee \sim q$ is true. $\sim p V \sim q$ is false.

Step 1 ：Let $p$ and $q$ represent the following statements: $p: 5+10=14$ and $q: 7 \times 3=42$.

Step 2 ：Determine the truth value for the statement $\sim p \vee \sim q$.

Step 3 ：The statement $p$ is false because $5 + 10$ does not equal $14$.

Step 4 ：The statement $q$ is also false because $7 \times 3$ does not equal $42$.

Step 5 ：Apply the NOT operation to each of these truth values. NOT false is true.

Step 6 ：Finally, apply the OR operation to these two truth values. The OR operation is true if either or both of its operands are true.

Step 7 ：So, the truth value of $\sim p \vee \sim q$ is true.

Step 8 ：Final Answer: $\sim p \vee \sim q$ is \(\boxed{true}\).