Discrete mathematics cardinality using Richard Hammacks

foass77W
2020-10-21
Answered

Discrete mathematics cardinality using Richard Hammacks

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Raheem Donnelly

Answered 2020-10-22
Author has **75** answers

Consider A is a superset of B and A is uncountable.
The objective to show that B is uncountable.
Assume B is countable.
Since using the concept that every subset of countable set is
countable.
So, A is countable.
Which is contradiction, as given A is uncountable.
Therefore, B is uncountable.
$\Rightarrow $ a superset of uncountable set is uncountable.
Hence proved.

asked 2021-08-02

Suppose that A is the set of sophomores at your school and B is the set of students in discrete mathematics at your school. Express each of these sets in terms of A and B.

a) the set of sophomores taking discrete mathematics in your school

b) the set of sophomores at your school who are not taking discrete mathematics

c) the set of students at your school who either are sophomores or are taking discrete mathematics

Use these symbols:$\cap \cup$

a) the set of sophomores taking discrete mathematics in your school

b) the set of sophomores at your school who are not taking discrete mathematics

c) the set of students at your school who either are sophomores or are taking discrete mathematics

Use these symbols:

asked 2021-08-15

How many elements are in the set
{ 0, { { 0 } }?

asked 2021-08-18

Discrete Mathematics Basics

1) Determine whether the relation R on the set of all Web pages is reflexive, symmetric, antisymmetric, and/or transitive, where$(a,b)\in R$ if and only if

I) everyone who has visited Web page a has also visited Web page b.

II) there are no common links found on both Web page a and Web page b.

III) there is at least one common link on Web page a and Web page b.

1) Determine whether the relation R on the set of all Web pages is reflexive, symmetric, antisymmetric, and/or transitive, where

I) everyone who has visited Web page a has also visited Web page b.

II) there are no common links found on both Web page a and Web page b.

III) there is at least one common link on Web page a and Web page b.

asked 2020-11-09

Use proof by Contradiction to prove that the sum of an irrational number and a rational number is irrational.

asked 2021-08-02

Using cardinatility of sets in discrete mathematics the value of N is real numbers

Currently using elements of discrete mathematics by Richard Hammack chapter 18

Let A be a collection of sets such that$X\in A$ if and only if $X\subset N$ and $\left|X\right|=n$ for some $n\in N$

Prove that$\left|A\right|=\left|N\right|.$

Currently using elements of discrete mathematics by Richard Hammack chapter 18

Let A be a collection of sets such that

Prove that

asked 2021-08-01

Discrete mathematics cardinality using Richard Hammacks

asked 2021-08-09

Let consider the following algorithm: Polynomial evaluation

This algorithm evaluates the polynomial

$P\left(x\right)=\sum _{k=0}^{n}{c}_{k}{x}^{n-k}$ At the point t.

Input: The sequence of coefficients$C}_{0},{C}_{1},\dots ,{C}_{n$ , the value tandn

Output: p(t)

Procedure poly(c, n, t)

If n=0 then

Return$\left({c}_{0}\right)$

Return$(t:poly(c,n-1,t)+{c}_{n})$

End poly

Let$b}_{n$ , be the number of multiplications required to compute p(t).

a) Find the recurrence relation and initial condition for the sequence$\left\{{b}_{n}\right\}$

b) Compute$b}_{1},{b}_{2}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}{b}_{3$ .

c) Solve the recurrence relation.

This algorithm evaluates the polynomial

Input: The sequence of coefficients

Output: p(t)

Procedure poly(c, n, t)

If n=0 then

Return

Return

End poly

Let

a) Find the recurrence relation and initial condition for the sequence

b) Compute

c) Solve the recurrence relation.