9. Show that (3 points each- 6 points) a. (p q) V (p - r) and p-(q Vr) are logically equivalert b. (-p ^ (p-+ q)) q is a tautology. A tautology is trivially true all the time. 10. Write the following sentences using universal and existential quantifiers. Clearly state the predicates in each problem. (2 point each 10 points) a. Every person has a friend. b. It is not the case that any student would get a good grade without studying c. Two persons are siblings if their parents are the same. d. There are happy moments in everyone's life. e. Some people in the community has cats, and some people have dogs f. Some students play computer games all the time. (bonus problem 1 point). g. It is not the case that a person can be happy and sad at the same time (bonus problem 1 point)