Question 9

(p _qpi (q p) c) p ^ q ^ r sq ^ p ^ r (commutative law) d) q)vrsps(q v r) (associative law) e) p ^ (q v r) (p ^ q) V (pm] (distributive law) f) Show truth table for DeMorgan's theorem (bonus problem 1 point 8. Use De Morgan's law to find the negation of the following sentences. 2 points each points) 4 a. John gets up before six and he gets in-time for the class b. Mary knows Discrete Structures or programming in 9. Show that (3 points each 6 points) a. (p-q) v (p r) and p- (q v r) are logically equivalent b. (- ^ (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 predica 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 5 6 8