# 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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...