Answer to Question #55966 in Discrete Mathematics for Bluxxy

Question

(1) In a lattice (L, ≤), prove the following (a) a∨(b∧c)=(a∨b)∧(a∨c)
(b) a∧(b∨c)=(a∧b)∨(a∧c)
(2) Consider the relation R = {(a, b) ∈ Z × Z , a|b} on Z. Check whether R is a partial order on
Z or not?
(3) The solution of the recurrence relation C0 ar + C1 ar−1 + C2 ar−2 = f (r) is 3r + 4r + 2. Given
that f(r) = 6 for all r, determine C0, C1, C2.
(4) Let ar =2r for all r
br =0 0≤r≤2 and br = 2r r ≥ 3
Find S−3(∇cr) and S3(∆cr) such that cr = ar ∗ br
(5) Use Quine Mccluskey method to simplify the Boolean expression
w ̄ x ̄ y z ̄ + w x y z + w x y ̄ z ̄ + w ̄ x y z ̄ + w ̄ x ̄ y ̄ z ̄ + w ̄ x y z + w x ̄ y z ̄ + w x y ̄ z + w x y z ̄ + w ̄ x y ̄ z + w x ̄ y ̄ z ̄ .

Answer 1

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