The question Is given below in figure:

13. Let the following statements be given. (a) Use connectives to translate the following statement into formal logic. If Andy is hungry and the refrigerator is empty, then Andy is mad. (b) Construct a truth table for the statement in part (a). (c) Suppose that the statement given in part (a) is true, and suppose also that Andy is not mad and the refrigerator is empty. Is Andy hungry? Explain how to justify your answer using the truth table. 14. Let A be the statement p - (q A -r). Let B be the statement q ~ r. (a) Construct truth tables for A and B. (b) Suppose statements A and B are both true. What can you conclude about statement p? Explain your answer using the truth table. 15. Use truth tables to prove the following distributive properties for propositional logic. (a) p A (q vr) is logically equivalent to (PAq) V (PAr). (b) pv (q Ar) is logically equivalent to (pv q) A (p vr)