Discrete Mathematics

QUESTION 8 Let Dao be the poset consisting of all the positive divisors of 30 under the partial order of divisibility (a) Write down the elements of Dao (2) (b) Draw the Hasse diagram of D30 (c) Is Dao a lattice? Give a reason for your answer (d) Give the complement of each element of D30 (e) Is Dao a Boolean algebra? Give a reason for your answer [13] QUESTION 9 Use a Karnaugh map to simplify the Boolen expression P(x, y, z) = (xAyz) V (x A y z) V(zny' Az) [5]