1. What is the truth value of (pq)(pq) when both p and q are false? 2. What are the converse and contrapositive of the statement "If it is sunny, then I will go swimming"? 3. Construct a truth table for each of these compound propositions. a) (pq)r b) (pq)r c) (pq)r d) (pq)r e) (pq)r f) (pq)r 4. Find the output of each of these combinatorial circuits. 5. An ancient Sicilian legend says that the barber in a remote town who can be reached only by traveling a dangerous mountain road shaves those people, and only those people, who do not shave themselves. Can there be such a barber? 6. Show that (pq) and qp are equivalent (a) using a truth table. (b) using logical equivalences. 7. Determine whether each of these compound propositions is satisfiable. a) (pqr)(pqs)(prs)(pqs)(pqs) b) (pqr)(pqs)(pqs)(prs)(pqr) (prs) 8. Suppose that Q(x) is the statement " x+1=2x." What are the truth values of xQ(x) and xQ(x)