Question 6

ry Bookmarks Window Help i) 78% CO Sat 3: 5. State the converse, contrapositive, and inverse of each of these conditional statements. Be sure to label them so it's clear which one is the converse, contrapositive, and the inverse. [each 2 point, total 20 points. There are nine statements (2 point each), and two points for neat labeling a) If it snows tonight, then I will stay at home. b) I go to the beach whenever it is a sunny summer day. c) When I stay up late, it is necessary that I sleep until noon. 6. Logical dircuits application: make a logical circuit to realize following logical expressions using combination of AND-gates, OR-gates, and inverter ( 10 points) a. p v(qAnb. (pAr. C. p q (bonus problem 2 points). One Approach: can be realized using combination of OR-gate and invert (AND-gate) and Section 1.3 to 1.5 (Quantifiers and DeMorgan's Theorem) 7. Use truth tables to verify the following laws. [each 2 points 10 points] a) p qE p v q (alternative way of witing implication) b) p qE (P ) A(q p) c)PAqAEqApAr(commutative law) d) (p v q) vrEpv (q v r) (associative law) e) pA qvr(p A q) V (PAr) (distributive law) 1) 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 MacBook Ai 30 5 7 8 9