# Tagged Questions

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### If $R$ is a transitive realation, then $R\circ R\subseteq R$

Here's the question I'm struggling with: Let R be a transitive relation on a set A. Prove the R composed with R is a subset of R. I'm kind of lost on how to prove this. I've started with saying: ...
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### Minimum score for winner and maximum score for loser in a round-robin tournament.

I have just correctly solved this programming problem. The problem is the following: $N$ teams play a round-robin tournament, i.e. each pair of teams plays exactly one game and the winner gets 3 ...
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### Prove $A = (A \setminus B) \cup (A \cap B)$

Prove $A = (A \setminus B) \cup (A \cap B)$ Logically, this is clearly true. I can explain why: start with $A$, remove all elements in $B$ and then add in any elements in both $A$ and $B$, which ...
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### How do we prove that, if $\mathcal{P}(A) \sim \mathcal{P}(B)$, then $A \sim B$? [duplicate]

The converse--if $\ A \sim B$ then $\mathcal{P}(A) \sim \mathcal{P}(B)$--is very easy to prove. I can't see an immediate, simple proof for the converse case. It seems like a potentially good strategy ...
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### Existence of a particular transformation

I've a set of data points $S = \{ x | x\in [0,1]\}$ (i.e. real values from the unit interval). In some cases I've big clusters in the data and I want to spread the values in between the unit interval ...
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### Prove that n!+1 contains a prime factor greater than n and use this to prove that there are infinte many primes [duplicate]

Prove that $n!+1$ contains a prime factor greater than $n$ and use this to prove that there are infinitely many primes. I said assume that $n!+1$ contains a prime $p$ which is less than or equal to ...
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### Disjunctive Normal Form (DNF) of a boolean combination

Upon revisiting chapter 1 of Robert S. Wolf's "A tour though mathematical logic" I sumbled upon the following Proposition on page 13 : Suppose that $P$ is a Boolean combination of ...
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### Show that if the diameter of an undirected graph is $d$ then there exists some vertex separator $S\subseteq V$ of size $|S| \leq { n\over d-1}$

Show that if the diameter of an undirected graph is $d$ then there is some set $S\subseteq V$ with $|S| \leq \frac{n}{d-1}$ such that removing the vertices in S from the graph would break it into ...
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