Discrete Mathematics Answers

8 If every element in a set is related to itself,the relation is said to be ________ relation.
reflexive
uniform
proportional
complex

9 If R and S are relations on A. What is R and S.
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A is empty
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10 What are the x-values called.
domain
function
symmetric
set

1 Any bunch of numbers is a _____ ,so long as the numbers come in pairs.
group
domain
axiom
relation

2 A ___ is just a set of ordered pairs.
sets
functions
partition
relation

3 Let N ={1,2,3,4,5, €¦ €¦ €¦.}, E = {2,4,6, €¦ €¦.}, F = {1,3,5, €¦ €¦..}. Then, {E,F} is a _____ of N.
functions
partition
relation
sets

4 A relation is a _____ ordering,if it is reflexive,anti- symmetric and transitive.
partial
complex
group
equal

5 A relation is a set of an ______ relation,if it is reflexive,transitive and symmetric.
simple
equal
balance
equivalence

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Title work is: Detective tasks or Application logic in solving problems.
If you can recommend a book, the author related to this subject.Well,I should use a few methods for that,but I don't have the explanation about these methods.
I look forward to hearing from you!

1. Expand the following Boolean functions into their canonical form:

i. f(X,Y,Z)=XY+YZ+ X' Z+ X' Y'
ii. f(X,Y,Z)=XY+ X' Y' + X' YZ

A book publisher has 3000 copies of a discrete mathematics
book. How many ways are there to store these books
in their three warehouses if the copies of the book are
indistinguishable?

A city has three newspapers A, B and C. Of the adult population, 1% read none of these newspapers. 36% read A, 40% read B, 52% read C, 8% read A and B, 11% read B and C, 13% read A and C and 3% read all the three newspapers. Required:
i. Illustrate the above information on a venn diagram
ii. What percent of the adult population read newspaper A only
iii. What percent of the adult population read newspaper B or Newspaper C
iv. What percent of the adult population read newspaper A or B but not C

(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 ̄ .