The statement given in the image is:

Construct a truth table for $\sim q \rightarrow \sim p$. Use T for true and F for false.

Here:

• $\sim q$ represents the negation of $q$,
• $\sim p$ represents the negation of $p$,
• $\rightarrow$ is the implication operator ("if... then...").

Let's break it down and construct the truth table step-by-step.

Explanation:

1. $p$ and $q$ take all combinations of True (T) and False (F).
2. $\sim p$ is the negation of $p$, and $\sim q$ is the negation of $q$.
3. The implication $\sim q \rightarrow \sim p$ evaluates to False only when $\sim q$ is True and $\sim p$ is False, and True in all other cases.

Would you like more detailed reasoning or explanations on any particular step?

Follow-up Questions:

1. What does the implication $\rightarrow$ represent in logic?
2. How does negation affect the truth values of propositions?
3. Can you apply this truth table to a real-world scenario involving conditions $p$ and $q$?
4. How would the truth table change if the operator were $\leftrightarrow$ (biconditional)?
5. Can you extend this truth table to include three variables (e.g., $p, q, r$)?

Tip:

When constructing truth tables, always start by listing all possible combinations of truth values for the variables involved.