1. The problem is to construct complete truth tables for the given logical statements involving propositions P, Q, and R. 2. Define the propositions: - P: Policies are implemented effectively. - Q: Public funds are managed properly. - R: The community benefits from the government program. 3. The statements to analyze are: 1. ~P (negation of P) 2. ~Q (negation of Q) 3. P ^ ~Q (P and not Q) 4. P ^ Q (P and Q) 5. (~P ^ ~Q) V α (alpha is unspecified, so we consider it as a variable or constant to be defined; assuming α as an extra proposition) 6. (P ^ Q) V [(~P ^ ~Q) V Q] 4. For truth tables, list all possible truth values of P and Q (assuming R is not directly involved in these expressions). Number of rows for the truth table with two variables (P, Q) is $2^2 = 4$. 5. Construct the truth table step by step: | P | Q | ~P | ~Q | P ^ ~Q | P ^ Q | ~P ^ ~Q | ( ~P ^ ~Q ) V α | (P ^ Q) V [(~P ^ ~Q) V Q] | |---|---|----|----|--------|--------|---------|----------------|--------------------------| Fill the columns: Row 1: P= T, Q= T ~P= F, ~Q= F P ^ ~Q= T ^ F= F P ^ Q= T ^ T= T ~P ^ ~Q= F ^ F= F Assuming α as T or F is unknown; treat α as variable. (~P ^ ~Q) V α= F V α= α (P ^ Q) V [(~P ^ ~Q) V Q]= T V [F V T]= T V T= T Row 2: P= T, Q= F ~P= F, ~Q= T P ^ ~Q= T ^ T= T P ^ Q= T ^ F= F ~P ^ ~Q= F ^ T= F (~P ^ ~Q) V α= F V α= α (P ^ Q) V [(~P ^ ~Q) V Q]= F V [F V F]= F V F= F Row 3: P= F, Q= T ~P= T, ~Q= F P ^ ~Q= F ^ F= F P ^ Q= F ^ T= F ~P ^ ~Q= T ^ F= F (~P ^ ~Q) V α= F V α= α (P ^ Q) V [(~P ^ ~Q) V Q]= F V [F V T]= F V T= T Row 4: P= F, Q= F ~P= T, ~Q= T P ^ ~Q= F ^ T= F P ^ Q= F ^ F= F ~P ^ ~Q= T ^ T= T (~P ^ ~Q) V α= T V α= T (P ^ Q) V [(~P ^ ~Q) V Q]= F V [T V F]= F V T= T 6. Interpretations: - ~P and ~Q are negations of P and Q - Conjunction (^) is AND - Disjunction (V) is OR 7. Summary: The truth table allows evaluation of the statements under all truth assignments for P and Q. Note: Since α is undefined, exact final values for statement 5 depend on α's truth value. Final answer: Truth tables constructed according to above details with consideration of α as variable.