a)

ringearV
2021-08-20
Answered

For each of the following sets A,B prove or disprove whether $A\subseteq B$ and $B\subseteq A$

a)$A=\{x\in Z:{\mathrm{\exists}}_{y\in z}x=4y+1\}$

$B=\{x\in Z:{\mathrm{\exists}}_{y\in z}x=8y-7\}$

a)

You can still ask an expert for help

Nathalie Redfern

Answered 2021-08-21
Author has **99** answers

Step 1

Given:

To prove or disprove:

Step 2

Counter Example:

Reason: Let

But

Therefore,

Step 3

Counter Example:

Reason: Let

But

Therefore,

asked 2021-08-02

Suppose that A is the set of sophomores at your school and B is the set of students taking 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: $\cap \cup$

asked 2021-07-28

Let A, B, and C be sets. Show that

asked 2021-08-18

Discrete Mathematics Basics

1) Find out if the relation R is transitive, symmetric, antisymmetric, or reflexive on the set of all web pages.where $(a,b)\in R$ if and only if

I)Web page a has been accessed by everyone who has also accessed Web page b.

II) Both Web page a and Web page b lack any shared links.

III) Web pages a and b both have at least one shared link.

asked 2021-08-15

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

asked 2022-07-18

A racketeer is allowed to bring no more than 3 of the 7 lawyers representing him to a Senate hearing. How many choices does he have?

This is what I have done but the correct answer is 64. I'm not sure how to get that answer.

$C(7,3)=\frac{7!}{3!4!}=35$

This is what I have done but the correct answer is 64. I'm not sure how to get that answer.

$C(7,3)=\frac{7!}{3!4!}=35$

asked 2022-09-04

Show that all rational numbers Q fit into the Hilbert hotel

Can I prove this with help of simple induction grounded on the basic axioms of number theory and a linearity pattern?

$$\frac{-x}{y}\ne \frac{x}{y}$$

$$\frac{-x}{-y}=\frac{x}{y}$$

The complete set of rational numbers according to me.

$$P=\{\frac{a}{b},[-\mathrm{\infty}\le (a,b)\le \mathrm{\infty}],\text{}a,b\in \mathbb{Z}\}$$

A subset of P is E.

E is a finite set with 50 unique elements. These elements fit in Hilbert's hotel.

$$E=\{\frac{a}{b},[-5\le (a,b)\le 5],\text{}a,b\in \mathbb{Z}\}$$

I derive the formula $r=10k$, where r is the amount of rooms needed.

$r=10k+10$, when $k+1$.

$$\{\frac{a}{b},[-k\le (a,b)\le k],\text{}a,b\in \mathbb{Z}\}$$

when k goes to infinty r goes to infinity. I have successfully counted the amount of rooms needed for an infinite amount of fractions. This only shows it's possible to fit them in the hotel. But in order to show how, do I need a function to map all fractions systematically?

Can I prove this with help of simple induction grounded on the basic axioms of number theory and a linearity pattern?

$$\frac{-x}{y}\ne \frac{x}{y}$$

$$\frac{-x}{-y}=\frac{x}{y}$$

The complete set of rational numbers according to me.

$$P=\{\frac{a}{b},[-\mathrm{\infty}\le (a,b)\le \mathrm{\infty}],\text{}a,b\in \mathbb{Z}\}$$

A subset of P is E.

E is a finite set with 50 unique elements. These elements fit in Hilbert's hotel.

$$E=\{\frac{a}{b},[-5\le (a,b)\le 5],\text{}a,b\in \mathbb{Z}\}$$

I derive the formula $r=10k$, where r is the amount of rooms needed.

$r=10k+10$, when $k+1$.

$$\{\frac{a}{b},[-k\le (a,b)\le k],\text{}a,b\in \mathbb{Z}\}$$

when k goes to infinty r goes to infinity. I have successfully counted the amount of rooms needed for an infinite amount of fractions. This only shows it's possible to fit them in the hotel. But in order to show how, do I need a function to map all fractions systematically?

asked 2022-07-16

I'm studying for my upcoming discrete math test and I'm having trouble understanding some equivalences I found in a book on the subject. I guess I'm not really familiar with these rules and I would like someone to walk me through the steps if they don't mind.

I know the elementary laws, De-Morgan's, absorption, distribution, associativity, symmetry, and idempotent laws. But I don't recognize how this person transforms the predicates. Could someone point out the name of the law I need to study?

The transformations are as follows:

$(not\text{}P\text{}and\text{}not\text{}Q)\text{}or\text{}(not\text{}Q\text{}and\text{}not\text{}R)$

$\Leftarrow \Rightarrow (not\text{}P\text{}or\text{}(not\text{}Q\text{}or\text{}not\text{}R))\text{}and\text{}(not\text{}Q\text{}or\text{}(not\text{}Q\text{}or\text{}not\text{}R))$

$\Leftarrow \Rightarrow (not\text{}P\text{}or\text{}not\text{}Q\text{}or\text{}not\text{}R)\text{}and\text{}(not\text{}Q\text{}or\text{}not\text{}Q\text{}or\text{}not\text{}R)$

$\Leftarrow \Rightarrow (not\text{}P\text{}or\text{}not\text{}Q\text{}or\text{}not\text{}R)\text{}and\text{}(not\text{}Q\text{}or\text{}not\text{}R)$

I know the elementary laws, De-Morgan's, absorption, distribution, associativity, symmetry, and idempotent laws. But I don't recognize how this person transforms the predicates. Could someone point out the name of the law I need to study?

The transformations are as follows:

$(not\text{}P\text{}and\text{}not\text{}Q)\text{}or\text{}(not\text{}Q\text{}and\text{}not\text{}R)$

$\Leftarrow \Rightarrow (not\text{}P\text{}or\text{}(not\text{}Q\text{}or\text{}not\text{}R))\text{}and\text{}(not\text{}Q\text{}or\text{}(not\text{}Q\text{}or\text{}not\text{}R))$

$\Leftarrow \Rightarrow (not\text{}P\text{}or\text{}not\text{}Q\text{}or\text{}not\text{}R)\text{}and\text{}(not\text{}Q\text{}or\text{}not\text{}Q\text{}or\text{}not\text{}R)$

$\Leftarrow \Rightarrow (not\text{}P\text{}or\text{}not\text{}Q\text{}or\text{}not\text{}R)\text{}and\text{}(not\text{}Q\text{}or\text{}not\text{}R)$