Recent questions in Indirect Proof

High school geometryAnswered question

jorgejasso85xvx 2022-11-19

Suppose that $\mathcal{U}$ is the universal set, and that $A$, $B$ and $C$ are three arbitrary sets of elements of $U$. Prove that if $C\beta \x88\x96A=B$, then the intersection of $A$ and $B$ is empty. Hint: use an indirect proof.

High school geometryAnswered question

piopiopioirp 2022-11-19

Prove the following through an indirect proof-

if $m+n$ is even, then $m$ and $n$ are even or $m$ and $n$ are odd.

if $m+n$ is even, then $m$ and $n$ are even or $m$ and $n$ are odd.

High school geometryAnswered question

Barrett Osborn 2022-11-18

Does proving that two lines are parallel require a postulate?

High school geometryAnswered question

Filloltarninsv9p 2022-11-15

Discrete math: proofs

For any three integers $\pi \x9d\x92\x99,\pi \x9d\x92\x9a$, and $\pi \x9d\x92\x9b$, if $\pi \x9d\x92\x9a$ is divisible by $\pi \x9d\x92\x99$ and $\pi \x9d\x92\x9b$ is divisible by $\pi \x9d\x92\x9a$, then $\pi \x9d\x92\x9b$ is divisible by $\pi \x9d\x92\x99$.

For any three integers $\pi \x9d\x92\x99,\pi \x9d\x92\x9a$, and $\pi \x9d\x92\x9b$, if $\pi \x9d\x92\x9a$ is divisible by $\pi \x9d\x92\x99$ and $\pi \x9d\x92\x9b$ is divisible by $\pi \x9d\x92\x9a$, then $\pi \x9d\x92\x9b$ is divisible by $\pi \x9d\x92\x99$.

High school geometryAnswered question

Kameron Wang 2022-11-04

Does ${x}^{2}\beta \x89\u20183$ (mod $q$) (where $q$ is an odd prime) have infinite solutions?

High school geometryAnswered question

Madison Costa 2022-11-02

Use an indirect proof to show that if ${x}^{3}+x\beta \x88\x921>10$ then $x>1$.

High school geometryAnswered question

Vincent Norman 2022-10-30

Prove for all positive real numbers $x$ and $y$, if $x+y\beta \x89\u20ac(4xy)/(x+y)$, then $x=y$

High school geometryAnswered question

Maverick Avery 2022-10-28

Prove the square root of $2$ is an irrational number.

High school geometryAnswered question

Paloma Sanford 2022-10-26

Why are direct proofs often considered better than indirect proofs?

High school geometryAnswered question

Winston Todd 2022-10-16

Let $a,b$ and $c$ be real numbers where $a>b$. Prove that if $ac\beta \x89\u20acbc$, then $c\beta \x89\u20ac0$.

High school geometryAnswered question

mafalexpicsak 2022-10-15

What is the negation of " $A\beta \x8a\x86B$ "?

High school geometryAnswered question

Aldo Ashley 2022-10-13

How to prove a function has no local minima.?

$f:{\mathbb{R}}^{2}\beta \x86\x92\mathbb{R}$ , of class ${C}^{2}$

$f:{\mathbb{R}}^{2}\beta \x86\x92\mathbb{R}$ , of class ${C}^{2}$

High school geometryAnswered question

vagnhestagn 2022-10-08

Let $G$be an acyclic graph with $c$ components. Show that the number of edges of $G$ is $n\beta \x88\x92c$.

High school geometryAnswered question

hikstac0 2022-10-07

Suppose ${x}_{1},{x}_{2},{x}_{3}\beta \x88\x88\mathbb{R}$. Prove that one of the ${x}_{i}$ must be greater than or equal to the average $\frac{1}{3}({x}_{1}+{x}_{2}+{x}_{3})$.

High school geometryAnswered question

Charlie Conner 2022-10-06

Prove that $\frac{2022}{n}+4n$ is a perfect square iff $\frac{2022}{n}\beta \x88\x928n$ is a perfect square

High school geometryAnswered question

Sincere Garcia 2022-10-03

If $(n+1{)}^{2}$ is even then $n$ is odd

find what proof works best with this question

find what proof works best with this question

High school geometryAnswered question

Diana Suarez 2022-09-27

Is it possible to prove directly that even perfect squares have even square roots? Or, symbolically:

$\mathrm{\beta \x88\x80}n\beta \x88\x88\mathbb{Z},\text{\Beta}\text{\Beta}{n}^{2}\text{\Beta is even\Beta}\beta \x87\x92n\text{\Beta is even\Beta}$ $\mathrm{\beta \x88\x80}n\beta \x88\x88\mathbb{Z},\text{\Beta}\text{\Beta}{n}^{2}\text{\Beta is even\Beta}\beta \x87\x92n\text{\Beta is even\Beta}$

$\mathrm{\beta \x88\x80}n\beta \x88\x88\mathbb{Z},\text{\Beta}\text{\Beta}{n}^{2}\text{\Beta is even\Beta}\beta \x87\x92n\text{\Beta is even\Beta}$ $\mathrm{\beta \x88\x80}n\beta \x88\x88\mathbb{Z},\text{\Beta}\text{\Beta}{n}^{2}\text{\Beta is even\Beta}\beta \x87\x92n\text{\Beta is even\Beta}$

High school geometryAnswered question

Medenovgj 2022-09-26

Let $Q(z)=(z\beta \x88\x92{\mathrm{\Xi \pm}}_{1})\beta \x8b\u2015(z\beta \x88\x92{\mathrm{\Xi \pm}}_{n})$ be a polynomial of degree $>1$ with distinct roots outside the real line.

We have

$\underset{j=1}{\overset{n}{\beta \x88\x91}}\frac{1}{{Q}^{\beta \x80\xb2}({\mathrm{\Xi \pm}}_{j})}=0.$

Do we have a proof relying on rudimentary techniques?

We have

$\underset{j=1}{\overset{n}{\beta \x88\x91}}\frac{1}{{Q}^{\beta \x80\xb2}({\mathrm{\Xi \pm}}_{j})}=0.$

Do we have a proof relying on rudimentary techniques?

High school geometryAnswered question

Melina Barber 2022-09-25

Suppose we have the following:

$P:.Qv\text{\Beta}Q$

Can this be proven without making assumptions for conditional or indirect proofs?

$P:.Qv\text{\Beta}Q$

Can this be proven without making assumptions for conditional or indirect proofs?

High school geometryAnswered question

gemauert79 2022-09-24

Proof the above premises and hypothesis using Indirect proof:

Premise $1$: $P\beta \x86\x92\mathrm{{\rm B}\neg}R$

Premise $2$: $Q\beta \x86\x92S$

Premise $3$: $(R\beta \x88\xa8S)\beta \x86\x92T$

Premise $4$: $\mathrm{{\rm B}\neg}T$

Hypothesis: $P\beta \x88\xa8Q$

Premise $1$: $P\beta \x86\x92\mathrm{{\rm B}\neg}R$

Premise $2$: $Q\beta \x86\x92S$

Premise $3$: $(R\beta \x88\xa8S)\beta \x86\x92T$

Premise $4$: $\mathrm{{\rm B}\neg}T$

Hypothesis: $P\beta \x88\xa8Q$

An indirect proof is a type of mathematical proof that uses a contradiction to prove that a statement is true. In other words, indirect proofs assume that the statement is false and then use reasoning to show that this leads to a contradiction. This type of proof is often used in geometry, as it can be difficult to directly prove certain geometric statements. Indirect proof can be challenging, but practice can help. Our online resource provides indirect proof problems and questions with answers and explanations. These can be a great way to learn and understand this type of proof.