# Tagged Questions

For questions about the formulation of a proof, not about the mathematics behind it.

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I would like to prove the statement that there are $2^{\binom{n-1}{2}}$ simple graphs are there with vertex set $\{1,\ldots,n\}$ such that every vertex has even degree. The thing that confuses me is ...
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### Writing a proof for $f(W) \setminus f(X) \subseteq f(W\setminus X)$

I am trying to write a proof to prove/disprove the following question: Will it always be true that $f(W\setminus X) = f(W)\setminus f(X)$? I know to prove this you need to show both ways since ...
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### $\mathcal B_{\mathbb Q}$ = = { [p, q) ⊆ R : p, q ∈ Q, p < q } is not a bases for the Lower Limit Topology

I'm having a bit of trouble proving this: The definition of Lower Limit Topology I am working with: $\{[a, b) \subseteq \mathbb R \ \text s.t \ a < b\}$. The only thing I can think of is that ...
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### Is this proof about the null space and column space correct?

My question asks me to show that if $A$ and $B$ are $n\times n$ matrices, and $AB=0$, then the column space of $B$ must be a subspace of the nullspace of $A$. My attempt at a proof is like this: we ...
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### Under what assumptions on φ is Tco-φ a topology

Fix a set X, and let φ be a property that subsets A of X can have. Define Tco-φ = {U ⊆ X : A = ∅, or X \ U has φ } . Under what assumptions on φ is Tco-φ a topology on X? What I think: 1. X\X has φ ...
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### Find the mistake of the following inductive proof: all algorithms have the same time complexity

I came across this problem: Find the mistake of the following inductive proof: Theorem: all algorithms have the same time complexity. Proof: (By induction on the number of algorithms.) The ...
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### Prove $A\setminus(B \cup C) = (A \setminus B) \cap (A \setminus C)$ using element chasing?

How can I prove $A \setminus(B \cup C) = (A \setminus B) \cap (A \setminus C)$ using element chasing? I need to verify that it is correct and show the steps of element chasing.
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### How to prove associative law for groups

I'm having trouble figuring out the proof to the proposition: for any $a_1,a_2,\ldots,a_n \in \mathbb{G}$ the value of $a_1~R~a_2~R~a_3~R\cdots R~a_n$ is independent of how the expression is bracketed ...
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### Are there other methods of proof other than contrapositive, induction, contradiction, construction, and counter example?

I have only heard of a few methods of proof, namely, contrapositive, induction, contradiction, construction, and counter example. Are there other types of proofs?
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### Proving function is convex argmin

How can I show that the following function is convex in which Z is a random variable? $$\rho(Z)=\frac{2}{3}argmin_{t}\{t+10\mathbf{E}[Z-t]_{+}\}+\frac{1}{3}argmin_{t}\{t+5\mathbf{E}[Z-t]_{+}\}$$ I ...
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### Proof that the Period of $\sin(x)$ is $2\pi$.

As I was walking through campus today, I had an interesting question pop into my head: How can we prove that the period of $\tan(x)$ is $\pi$ rather than $2\pi$? The answer to this was extremely ...
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### Vector subspace and linear application proof

I would like to know if my proof is correct and, moreover, if it is well written. Let $E$ and $F$ be vector subspaces and $f: E \to F$ an application. Proof that, if $U$ is a vector subspace of $E$...