Discrete math Question.

Suppose your friend makes the following English statement "If

Bergen
2021-08-21
Answered

Discrete math Question.

Suppose your friend makes the following English statement "If

You can still ask an expert for help

Dora

Answered 2021-08-22
Author has **98** answers

Step 1

The symbol

Step 2

To convert the English statement to a statement, write it in mathematical form by removing if and then. Also remove all other texts in statements. This will give the statement :

To check the validity of the statement make a truth table with each entry. The first column will be X then Y followed by the operations.

Step 3

The value of

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.

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

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

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 2021-05-05

Consider a Poisson process on

asked 2022-06-26

Clever proof for showing that if a graph G is critically k-colorable then $\delta (G)\ge k-1$

While reading for my graph theory class, I came across a short - yet curious - proof for the following theorem: if a graph G is critically k−colorable then $\delta (G)\ge k-1$. Here is the proof to the claim:

Suppose (for a contradiction) that G is k-critical and that $v\in V(G)$ satisfies $\text{deg}(G)<k-1$. Then $G-v$ has a $(k-1)-$ coloring, and this coloring extends to a $k-1$- coloring of G. This yields a contradiction.

Everything in this proof makes sense besides one particular item: in the second line, what does the author mean by extending a coloring from a subgraph of G to the whole graph? In addition, why does $G-v$ have a $(k-1)$ coloring that extends to all of G (if that makes any sense)? I understand this may seem like an easy Google search but to be honest I can't find anything helpful and figured someone could provide some insight.

Note that this is not a homework question but simply for going beyond what I am learning in class.

While reading for my graph theory class, I came across a short - yet curious - proof for the following theorem: if a graph G is critically k−colorable then $\delta (G)\ge k-1$. Here is the proof to the claim:

Suppose (for a contradiction) that G is k-critical and that $v\in V(G)$ satisfies $\text{deg}(G)<k-1$. Then $G-v$ has a $(k-1)-$ coloring, and this coloring extends to a $k-1$- coloring of G. This yields a contradiction.

Everything in this proof makes sense besides one particular item: in the second line, what does the author mean by extending a coloring from a subgraph of G to the whole graph? In addition, why does $G-v$ have a $(k-1)$ coloring that extends to all of G (if that makes any sense)? I understand this may seem like an easy Google search but to be honest I can't find anything helpful and figured someone could provide some insight.

Note that this is not a homework question but simply for going beyond what I am learning in class.

asked 2021-08-11

Discrete math

Let$A=\{2,4,5,7,9\}$ . Choose the correct statement from the below.

Select one:

1)$2\subset A$

2)$5\in A$

3)$1\in A$

4) A is not a set.

Let

Select one:

1)

2)

3)

4) A is not a set.