Questions tagged [solution-verification]

For posts looking for feedback or verification of a proposed solution. "Is my proof correct?" is too broad or missing context. Instead, the question must identify precisely which step in the proof is in doubt, and why so. This should not be the only tag for a question, and should not be used to circumvent site policies regarding duplicate questions.

This tag should be used when you have a proposed solution to a problem and have specific concerns or doubts about the validity of that solution. A question with this tag should include an explanation for why the argument presented is not convincing enough. Further discussion on using this tag can be found in the Mathematics Meta questions (1) and (2).

Answers to questions tagged look first and foremost to check that the solution is right, and to comment upon the approach taken by the author of the question. If the proposed solution is wrong, a good answer would explain where or how mistakes were made, and possibly give or sketch a correct solution instead.

If the proposed solution is correct, an answer would ideally provide further evidence to back the answerer's opinion. These could include a clearer rewriting of the given argument, alternative arguments, generalizations of the proven result, or careful consideration of unexpected subtle points. Users looking to write answers can find further discussion in this Mathematics Meta post.

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rules of inference help

Let p, q, r, s and t be statements variables. Use the valid argument forms to deduce the conclusion, ¬q, from the premises, giving a reason for each step. (a) ¬p ∨ q → r. (b) s ∨ ¬q (c) ¬t (d) p → t (e) ¬p∧r → ¬s —————————————————— (f) ∴ ¬q I have…
Ronald
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Proof of integral identity

I was looking for a proof of this identity: \begin{equation} \int_{\mathbb{R}^n}\phi \Delta\phi = - \int_{\mathbb{R}^n}|\nabla\phi|^2 \end{equation} given $\phi \in C_0^{\infty}(\mathbb{R}^n)$.
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Prove that there are at least two points a, b ∈ [0, 2] whose distance is equal to 1 and for which h (a) = h (b) is verified

I have been thinking about this problem but I am not able to find a solution. Ler h be a continuous function in the range [0, 2] and such that h (0) = h (2). Prove that there are at least two points a, b ∈ [0, 2] whose distance is equal to 1 and for…
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Prove that If x and y are integers and x + y is odd , then x−y is odd.

I am facing a problems with this question : Prove that If x and y are integers and x + y is odd , then x−y is odd. , any suggestions ?
me22
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Proof verification for $A$ $\times$ $B$ $\subseteq$ $\bigcup$ $\mathcal{F}$ $\otimes$ $\mathcal{G}$

Suppose $\mathcal{F}$ is a partition of $A$ and $\mathcal{G}$ is a partition of $B$. Let $\mathcal{F}$ $\otimes$ $\mathcal{G}$ be defined as follows: $$\mathcal{F} \otimes\mathcal{G} = \{Z \in \mathscr{P}(A\times B) \mid (\exists X)(\exists Y)(X\in…
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How do you prove by mathematical induction that $n(n+2)$ is divisible by $8$, if n is even and greater than 1

Everything is ok except for when I try to substitute $n = k + 1$. I get $8J + 4k + 8$ (where J is an integer) and cannot further factorize out an 8 to prove it is divisible. Is this even a correct substitution?
user71207
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Number of ways to draw non-intersecting lines in a circle.

Given 10 points in a circle, in how many ways can you draw 5 lines so that all points are part of exactly one line and no line intersects another line? An example of a solution can be: enter image description here The solution according to a paper…
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MAT 2003 Oxford Admissions Exam Question 5 Solution Verification

As ongoing trend, I have been solving old MAT past papers that do not have published solutions. I was wondering if anybody can verify my solution to the following question. My Solution (i) We prove this by contradiction. Suppose that after one…
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Why does this "proof" fail to show rationals are uncountable?

I know that rationals are countable, but I'm not seeing the flaw in this reasoning showing that rationals are uncountable: We start by defining $f:\Bbb N \to \Bbb Q$ such that $$ 1 \mapsto \frac{p_1}{q_1}\\ 2 \mapsto \frac{p_2}{q_2}\\ 3 \mapsto…
Badr B
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Solving for the normal distribution

Given that 40% of our toys weigh between $\mu$ and $\mu + 30$ where $\mu = 230 \text{grams}$ and their weight is distributed normally. Then what is the Standard deviation ? My way: I moved to standard normal dist. $ Z = \frac{X - 230}{ s}$ and know…
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For all $A, B \in\Bbb Z$, if $A\mid B$ and $B\mid A$, then $A =B$.

I know this is a simple question, but I am struggling a bit. What I have so far is. Let $A, B$ be arbitrary elements in $\Bbb Z$ and assume $A\mid B$ and $B\mid A$ is true. $A=B \Rightarrow \dfrac{A}{B}=\dfrac{B}{B} \Rightarrow \dfrac{A}{B} =1$ …
user803476
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Is it possible that some proofs are using trickery?

I had a thought about how one might fake a proof or indeed fool yourself that you have proved something. First take the proof and convert it into an equivalent question in a field of mathematics that is very obscure and not many people work on.…
zooby
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Proof Verification of showing continuity of a function

This is a problem from Fitzpatrick 2nd edition Advanced Calc textbook. Consider: \begin{equation*} f(x) = \begin{cases} x^2 & x \leq 0 \\ x+1 & x > 0 \end{cases} \end{equation*} Where is f continuous? Proof (by…
thomasbdc
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Matrix norm inequalities for 2-norm and $\infty$-norm

I am doing the following exercise: https://i.stack.imgur.com/Ye9C3.png I proved parts $a$ and $b$, but I got a little confused with parts $c$ and $d$. Here is my proof for part $(c)$: Let $x \in \mathbb{R}^{n}$ and view $A$ as a $mn$-dimensional…
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Can I rewrite this statement "Let $x,y$ $\in$ $5\mathbb{Z}$. prove that $x+y$ $\in$ $5\mathbb{Z}$ ." like this?

How to rewrite this problem? I have a problem. "Let $x,y$ $\in$ $5\mathbb{Z}$. prove that $x+y$ $\in$ $5\mathbb{Z}$ ." I did try to write this problem in the form of "something is an element of (set builder notation)" like this. prove that $x+y$…