Improve Indirect Proof: Examples & Tips

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

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.

Barrett Osborn 2022-11-18

Does proving that two lines are parallel require a postulate?

Filloltarninsv9p 2022-11-15

Discrete math: proofs
For any three integers $𝒙, 𝒚$ , and $𝒛$ , if $𝒚$ is divisible by $𝒙$ and $𝒛$ is divisible by $𝒚$ , then $𝒛$ is divisible by $𝒙$ .

Kameron Wang 2022-11-04

Does $x^{2} \equiv 3$ (mod $q$ ) (where $q$ is an odd prime) have infinite solutions?

Madison Costa 2022-11-02

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

Vincent Norman 2022-10-30

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

Maverick Avery 2022-10-28

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

Paloma Sanford 2022-10-26

Why are direct proofs often considered better than indirect proofs?

Winston Todd 2022-10-16

Let $a, b$ and $c$ be real numbers where $a > b$ . Prove that if $a c \leq b c$ , then $c \leq 0$ .

mafalexpicsak 2022-10-15

What is the negation of " $A \subseteq B$ "?

Aldo Ashley 2022-10-13

How to prove a function has no local minima.?
$f : R^{2} \to R$ , of class $C^{2}$

vagnhestagn 2022-10-08

Let $G$ be an acyclic graph with $c$ components. Show that the number of edges of $G$ is $n - c$ .

hikstac0 2022-10-07

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

Charlie Conner 2022-10-06

Prove that $\frac{2022}{n} + 4 n$ is a perfect square iff $\frac{2022}{n} - 8 n$ is a perfect square

Sincere Garcia 2022-10-03

If $(n + 1)^{2}$ is even then $n$ is odd
find what proof works best with this question

Diana Suarez 2022-09-27

Is it possible to prove directly that even perfect squares have even square roots? Or, symbolically:
$\forall n \in Z, n^{2} is even \Rightarrow n is even$ $\forall n \in Z, n^{2} is even \Rightarrow n is even$

Medenovgj 2022-09-26

Let $Q (z) = (z - α_{1}) \dots (z - α_{n})$ be a polynomial of degree $> 1$ with distinct roots outside the real line.
We have
$\sum_{j = 1}^{n} \frac{1}{Q^{'} (α_{j})} = 0.$
Do we have a proof relying on rudimentary techniques?

Melina Barber 2022-09-25

Suppose we have the following:
$P : . Q v Q$
Can this be proven without making assumptions for conditional or indirect proofs?

gemauert79 2022-09-24

Proof the above premises and hypothesis using Indirect proof:
Premise $1$ : $P \to \neg R$
Premise $2$ : $Q \to S$
Premise $3$ : $(R \lor S) \to T$
Premise $4$ : $\neg T$
Hypothesis: $P \lor Q$

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.

Learn Indirect Proof with Plainmath's In-Depth Explanations and Real-World Examples