Simple discrete math proof.

Prove that if $a,b\in {\mathbb{Z}}^{+}$, that a|b and b|a, then $a=b$

Prove that if $a,b\in {\mathbb{Z}}^{+}$, that a|b and b|a, then $a=b$

Luciano Webster
2022-07-15
Answered

Simple discrete math proof.

Prove that if $a,b\in {\mathbb{Z}}^{+}$, that a|b and b|a, then $a=b$

Prove that if $a,b\in {\mathbb{Z}}^{+}$, that a|b and b|a, then $a=b$

You can still ask an expert for help

Jeroronryca

Answered 2022-07-16
Author has **13** answers

Step 1

I guess there's multiple ways to go about proving the above question. The simplest:

$a|b\to a\le b\phantom{\rule{0ex}{0ex}}b|a\to b\le a$

Step 2

Considering the fact that a,b are both positive it follows that $a=b$.

I guess there's multiple ways to go about proving the above question. The simplest:

$a|b\to a\le b\phantom{\rule{0ex}{0ex}}b|a\to b\le a$

Step 2

Considering the fact that a,b are both positive it follows that $a=b$.

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.

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

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

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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:

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How to prove this inequality with the simplest means?

${x}^{2}+5{y}^{2}+6{z}^{2}\ge 4\sqrt{5xy{z}^{2}},\text{}\text{if}\text{}xy0$

I was trying to prove it. The right hand side should be nonnegative, so I can square it on both sides. But once I have done it I get to a point, where I do not see how to show, that the statement is greater or equal to 0.

${x}^{4}+25{y}^{4}+36{z}^{4}+10{x}^{2}{y}^{2}+12{x}^{2}{z}^{2}+60{y}^{2}{z}^{2}-80xy{z}^{2}\ge 0.$.

${x}^{2}+5{y}^{2}+6{z}^{2}\ge 4\sqrt{5xy{z}^{2}},\text{}\text{if}\text{}xy0$

I was trying to prove it. The right hand side should be nonnegative, so I can square it on both sides. But once I have done it I get to a point, where I do not see how to show, that the statement is greater or equal to 0.

${x}^{4}+25{y}^{4}+36{z}^{4}+10{x}^{2}{y}^{2}+12{x}^{2}{z}^{2}+60{y}^{2}{z}^{2}-80xy{z}^{2}\ge 0.$.

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Show that if $S1\subseteq S2$, then $\overline{{S}_{2}}\subseteq \overline{{S}_{1}}$ (the complement of S2 is the subset of the complement of S1)

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