Discrete Mathematics Answers

Solve the recurrence relation a_n-4a_n-1+5a_n-2-2a_n-3=1+2^n

Solve the recurrence relation term an-4(term an-1)+5 term an-2- 2 term an-3=1+2^n

Prove the following result by contradiction:
Let f : X TO Y be a mapping. Suppose f (A INTERSECTION B) = f (A) INTERSECTION f (B) for all subsets
A, B PROPER SET X , f (PHI) = PHI. Then f is a 1-1 mapping.

4. If the roots of the cubic az3 + bz2 + cz + d = 0 form an arithmetic progression α − β,
α, α + β, prove that (2b
2 − 9ac)b + 27a
2d = 0.

Given the function F (X, Y , Z)=Σm(0,1, 2 , 4 , 6)

answer the following questions:

1. Obtain the expression in the Canonical Disjunctive Normal Form

2. Obtain the expression in the Canonical Conjunctive Normal Form

3. Derive the truth table for both the Minterms and Maxterms

4. Obtain the minimized SOP and POS

5. Draw the resultant circuit diagram for the minimized SOP

You are required to provide your solution on a separate file and attach it.

Let A={2,3,6,12}and let R and S be the following relations on A. xRyiff 2 / x–y, xSyiff 3 / x–y. Compute the following R^---,R^S,R U S,S^-1

Determine the following relation is an equivalence relation or not. If the relation is an equivalence relation, describe the partition given by it. x~y in R if |x-y|<4

Draw the Hasse diagram for divisibility on the set {1,2,3,4,6,8,12}. Do the maximal, minimal elements exist? If so, what are they? What is the greatest element?

Determine the following relation is an equivalence relation or not. If the relation is an equivalence relation, describe the partition given by it. m~n in Z if m=n mod 6. 51. Which of them are equivalence relations?
(a) "less than" on the set N
(b) "has the same shape as" on the set of all triangles

Prove that the relation ‘’Superset of ’’ is a partial order relation on the power set of S.