# Questions tagged [discrete-mathematics]

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.

22,036 questions
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### Question regarding partially ordered sets

I have encountered few questions while reading the book 'Modern Algebra'. Let $\mathbb Q$ be the set of rational numbers. Let $B = \{ x : x\in\mathbb Q,\sqrt2 < x < \sqrt3 \}$. How it can ...
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### Number of eulerian paths in an undirected connected graph between two given vertices?

Given a undirected connected graph G(V, E). Provide an optimal algorithm, which finds the number of eulerian paths between vertex 1 and vertex |V|. I was thinking about matrix multiplication, but I ...
1answer
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### Finding n in equivalence between two permutations

Find the value(s) of n: 2P(n, 2)+50 = P(2n, 2) For 2P(n, 2)+50 I simplified to 2(n)(n-1)+50. For P(2n, 2) I can't get any simpler than $2n\times(2n-1)\times...\times(n+1)\times n\times(n-1)$ and I'm ...
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### Construct a rank-3 matroid using rank-2 flat

Let $E$ be a finite set with size bigger or equal to 3. Let $L$ be a collection of subsets of $E$ such that: $2 \leq |A| < |E|$ for any $A \in L$ $|A \cap B| \leq 1$ for any $A, B \in L$ Now show ...
2answers
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### Number of students and how many are taking X class (Discrete Structures)

So I have my first quiz tomorrow and want to get off on the good foot, but I'm studying some problems and this one is particularly confusing... There are a group of 191 students, of which 10 are ...
2answers
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### Uniform discrete distribution - time to draw

I have a question about the basic definition of discrete normal distribution. Let's assume I have a machine that draws a number ranging from 1 to 3 from a uniform discrete distribution (the ...
0answers
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### Prove that every planar graph is the union of at most $5$ acyclic graphs.

Prove that every planar graph is the union of at most $5$ acyclic graphs. Reminder: As union of two graphs $G_1(V_1, E_1)$ and $G_2(V_2, E_2)$ we consider the graph $G(V_1\cup V_2,E_1\cup E_2)$ ...
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### Show that the second player can always achieve a draw in the defined game

currently at it working on my discrete mathematics assignment, where I now have one assignment, that I just can't crack. I feel like I am very close, but miss something critical to it. So, I have the ...
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### For all sets $A, B, C$, If $A \Delta B = A \Delta C$, then $B \subseteq C$

I get the general reason as to why this is True. I'm just having trouble trying to formulate this into a logically correct proof. My approach was: (1) Assume $A \Delta B = A\Delta C$ (2) Let $x$ be ...
1answer
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### probabilility point closer to distance circle

the probability that the point is closer to the distance to the center of the circle than to the circumference is $\frac{1}{4}$ find probability: (A) When several points are selected sequentially ...
0answers
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### Way of predicting change in gradient of line following matrix transformation?

I recently learnt about dominant and repulsive eigenvectors. I noticed that the farther a line is initially from the dominant (though still closer than to the repulsive eigenvector), the more dramatic ...
2answers
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### Proof that the sum of all degrees is equal to twice the number of edges

We want to proof $2|E| = \sum \limits_{v \in V} deg(v)$ for a simple graph (no loops). For our proof we assume $n$ to be the number of edges in a simple graph $G(E, V)$. We proceed our proof by ...
2answers
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### For $(a + b + c + d)^{10}$, how many terms have coefficients that aren't divisible by $5$?

$(a + b + c + d)^{10}$ how many terms have coefficients that aren't divisible by $5$? I know that each of the following $a^{10}, b^{10}, c^{10}, d^{10}$, their coefficient is 1, which isn't ...
2answers
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### Permutation from left to right of $140$ objects

I've been stuck on this problem for quite some time now, I can't seem to find a video or such where it references permutations in a specific order of left to right. I have no idea how to set this ...
1answer
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### Find the time gap between two vehicle based on km/h of the vehicle

I am currently researching on VANET for identifying the road capacity based on vehicle moving speed. Below is my question, If a car moving on 8km/h and distance to the next car is 15 meters, what ...
1answer
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### Expected value of the number of different numbers drawn in 37 rounds of roulette?

I need help with this problem. What is the expected value of the number of different numbers drawn in 37 rounds of roulette? Is this possible to interpret as the number of records? So the expected ...