Construct a truth table for the given statement. \[ \sim(\sim q \vee p) \]

Step 1 ：Given the logical statement ¬(¬q ∨ p), we are asked to construct a truth table. This involves the logical operations of negation (¬), disjunction (∨), and conjunction (∧).

Step 2 ：A truth table is a mathematical table used in logic to compute the functional values of logical expressions on each of their functional arguments. It shows the output values for all possible input combinations.

Step 3 ：In this case, we have two variables, p and q, so there are 2^2 = 4 possible combinations of truth values for p and q: (True, True), (True, False), (False, True), and (False, False).

Step 4 ：We will first calculate the truth values for ¬q and p, then for ¬q ∨ p, and finally for ¬(¬q ∨ p).

Step 5 ：The truth table for the logical statement ¬(¬q ∨ p) is: \[\begin{array}{cccc} p & q & ¬q ∨ p & ¬(¬q ∨ p) \\ \hline \text{True} & \text{True} & \text{True} & \text{False} \\ \text{True} & \text{False} & \text{True} & \text{False} \\ \text{False} & \text{True} & \text{False} & \text{True} \\ \text{False} & \text{False} & \text{True} & \text{False} \\ \end{array}\]

Step 6 ：\(\boxed{\text{Final Answer: The truth table for the logical statement ¬(¬q ∨ p) is:}}\) \[\begin{array}{cccc} p & q & ¬q ∨ p & ¬(¬q ∨ p) \\ \hline \text{True} & \text{True} & \text{True} & \text{False} \\ \text{True} & \text{False} & \text{True} & \text{False} \\ \text{False} & \text{True} & \text{False} & \text{True} \\ \text{False} & \text{False} & \text{True} & \text{False} \\ \end{array}\]