# Tagged Questions

The study of discrete mathematical structures. Consider using a more specific tag instead, such as: (combinatorics), (graph-theory), (computer-science), (probability), (elementary-set-theory), (induction), (recurrence-relations), etc.

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### Spanning trees of the complete graph minus two edges

Here is the following problem: What two edges should one remove from the complete graph $K_n$ so that the number of the spanning trees of the new graph is as small as possible? One can solve this ...
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### Predicate Calculus help

Working on predicate calculus this week, and was hoping I've got these correct, but I'm sure I've made some mistakes for sure.. All programmers enjoy discrete structures not all integers are ...
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### Calculus for Proving Properties of Discrete Objects

I posted a question earlier about a proof in graph theory I was trying to figure out. In my attempt I used Calculus to prove a part of the theorem. In the comments people kept saying how you shouldn't ...
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### Counting the number of Eulerian trails in a connected, directed graph

I can't find anything about this online, and I'm beginning to suspect it's a hard problem. I know that counting the number of circuits is #P-complete, but I don't need the number of circuits; I need ...
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### Need help understanding a proof (Bipartite Graph)

I was reading lecture notes of graphs(from MIT 6042) and am having trouble understanding this proof: I can't understand ...
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### recursive definition for two mutually exclusive events [on hold]

How do we write recursive definitions for two mutually exclusive events ? Can anyone explain with some examples as how do we come up with solutions in case of exclusive events ? SO finally i add ...
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### What algebra of propositions will prove the obvious?

I am trying to use the algebra of propositions to prove the following. It is obviously true but I am stumped as to what algebra of proposition to use to show a sound mathematical explanation as a ...
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### If $f:A\to P(A)$, show that $Z_f := \{x \in A | x \notin f(x)\}$ is not in the Image of $f$

How can I prove that for a function $f: A \to P(A)$, $Z_f := \{x \in A | x \notin f(x)\}$ is not in the Image of f? It can be shown using Russel's Paradox, but i have really no clue on how to start. ...
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### Showing properties of a function and its inverse image

I tried proving the following question but did not get too far. Let $\ f:A \to B$ be a function and $\ f^{-1}(Y)$ be the inverse image of $\ Y\subseteq B$ on $\ f$. Consider the following ...
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### Proving set theory subsets using element argument

How do you even prove a set theory subset statement using element argument? I simply just can't find any relevance to the question with the notes i was studying. Any guidance would be much ...
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### Simplifying $(A \cup E) \cup E$.

For example $$(A^c\cap B^c)^c\cup E$$ First of all, De Morgan is definitely a must to simply this to $$\big((A^c)^c\cup(E^c)^c\big)\cup E$$ Then double negation to remove the double complement to ...
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### A question in set theory about intersection of two groups.

I've reached the answer, that Cn = to all prime numbers, but i really didnt know how to put it on paper and how to prove its right. I would thank your help.(question below) Question
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### A simple discrete math riddle [on hold]

Let P be a set of integers. Let N be the number of the elements in P. Prove that there must be a subset of P that it's sum is divided by N. Any idea?
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### Discrete Math Understanding a proof involving the definition of divisibility

In this first course on discrete mathematics, the instructor provided this following solution to a question. The question was asked us to prove the following (the solution is provided as well): My ...
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### Need to prove that there is a continuous sequence which contains 100 cup of coffee , i.e. a man drinks one cup of coffee at the day.

A man can drink at least one cup of coffee at the day. After one year he drinks 500 cup of coffee. Need to prove that there is a continuous sequence which contains 100 cup of coffee, i.e. a man drinks ...
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### Let K be an integer between $800,000$ and $900,000$ so that (Greatest Common Divisor) [on hold]

Let K be an integer between $800,000$ and $900,000$ so that,$\gcd(K,271)>\gcd(K,2016)>100$. List all values of K. Need serious help with this!!! Respond asap, please!
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### Help solving this recurrence relation

I wanted to resolve the determinant of the next (nxn) matrix via recurrence relations:  \begin{vmatrix} a & 1 & 0 & 0 & 0 & 0 &.... 0 & 0 & 0 & 0 & 0\\ 1 &...
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### maximum number of edges given diameter and number of vertices [on hold]

Let us assume that $G = (V,E)$ is an undirected unweighted simple graph. Let $d$ is the diameter of the graph $G$, $n$ is the number of vertices, and $m$ is the number of edges. Now I am looking for ...
Let $S$ be the set of all positive divisors of $30$. Prove that $(S,\le)$ a poset where $a\le b$ means a is a divisor of $b$, for $a,b \in s$.