Discrete Mathematics Answers

0. a) Find the solution of the difference equation yk+2 − 4yk+1 + 4yk = ;0 k = ,1,0 K. Also find
the particular solution when 1 y0 = and 6 y1 = .

What makes A = {1,2,4,5} and B = {2,3,6,7} not disjoint

The Cartesian product (A x B) of the sets A and B is the set of

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

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 The technique of determining an approximate value of f(x) for a non-tabular value of x which lies outside the internal [a, b] is known as............
a. Newton’s second law
b.Newton’s first law
c. Interpolation
d. extapolation

2 The Lagrange’s interpolating polynomial P(x) is given by …………..
a. P(x)=L 0 (x)f 3 +L 1 (x)f 2 +L 2 (x)f 1 +L 3 (x)f 0
b. p(x)=L 1 (x)f 0 +L 2 (x)f 1 +L 3 (x)f 2 +L 4 (x)f 3
c. P(x)=L 0 (x)f 0 +L 1 (x)f 1 +L 2 (x)f 2 +L 3 (x)f 3
d. P(x)=L 0 (x)f 0 +L 1 (x)f 2 +L 2 (x)f 2 +L 3 (x)f 3

The OR gate have a Boolean mathematical equivalence of _________
Multiplication
Inversion
Negation
Addition