# 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.

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### Let $R=\{(x,y)∈ℝ^2; x^2 <= y^2\}$. Give an infinite subset of $X$ of $ℝ$, such that $R∩X^2$ defines a total order of X.

Hi can anyone help me with the following question? Let $R=\{(x,y)∈ℝ^2; x^2 <= y^2\}$. Give an infinite subset of $X$ of $ℝ$, such that $R∩X^2$ defines a total order of X.
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### Expected number of fixed points in a permutation by brute force

I'm trying to compute the expected value of fixed points in a permutation without using the linearity of expectation. I tried the following: $$\sum_{i=1}^{n} i\frac{(n-i)!\binom{n}{i}}{n!}$$ However, ...
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### how do i solve non linear equation? TOPIC IS PDE [closed]

Find a separated solution of the following nonlinear wave equation: ∂u/∂t=cu ∂y/∂x and What is a separated solution of the 2 -dimensional wave equation (∂^2 u)/(∂t^2 )=a (∂^2 u)/(∂x^2 )+b (∂^2 u)/(∂y^...
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### How to prove the following statement regarding the successor function and addition of natural numbers?

Natural numbers (including 0) and the successor function are defined as per the Peano Axioms (you can check them on wikipedia). Addition is defined recursively as follows: $a+0=a$ $a+S(b)=S(a)+b$ With ...
27 views

### Math struggles for discrete math and Linear algebra [closed]

I am a second year student at a community college. I have autism and obsessed with my grades. I am struggling heavily when comes to these mathematics. I have tried youtube, my classmates, and my ...
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### series development problem, binomial theorem. Need ideas how to solve it [duplicate]

Need ideas about how to solve this task. The problem is based on series development and I have a problem getting the idea of what to do in this task
61 views

### Using a generating function to solve a recursion

I know that the generating function for the sum of Fibonacci numbers with even index is \begin{align} F_e(z) &= \sum_{n \ge 0} F_{2 n} z^n \\ &= \frac{F(z^{1/2}) + F(- z^{1/2})}{2} \\ &...
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### Probability that at least $6$ of $10$ randomly drawn light bulbs are white [closed]

Out of $100$ bulbs produced by a manufacturing company, $35$ are white light bulbs and the rest are yellow light bulbs. If $10$ bulbs are randomly drawn without replacement, find the probability that ...
62 views

### Question about number of generating functions

I know that the generating function for the number of integer partitions of $n$ into distinct parts is $$\sum_{n \ge 0} p_d(n)x^n = \prod_{i \ge 1}(1+x^i)$$ I'm trying to use this generating function ...
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### Can a Probability Distribution be made of Discrete Variables?

I have been trying to determine the popular "consensus" as to how mixed continuous and categorical data (e.g. a dataset that has variables on income and gender) is generally analyzed in the ...
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### You will get an A in this class if and only if you either do every exercise in this book or you get an A on the final? [closed]

I need an answer for this question.
1 vote
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### Placing $n$ rooks peacefully on a board

We got $n\times n$ board colored in different colors. The count of cells with the same color is $\leq \frac{n-1}{16}$. Prove that we can manage to place $n$ rooks on different color cells, so they ...
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### Problem related with mathematical inductions [duplicate]

Show that n^2 > 2n +1 for n >= 3 by the mathematical induction I have tried (k+1)^2 > 2(k+1) + 1 and I am stuck hereafter
1 vote
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### Absolute value on addition [closed]

Does the absolute value is distributive over addition or in other some way abs(3x)+abs(1-x)=abs(2-4x) can we here collect the terms on the left hand side inside on absolute value. i.e abs(3x+1-x)=...
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### How to calculate the orthogonality error between sine and cosine wave?

As the picture below(assume the magnitude is the same),the zero-crossing points of the SIN and COS signals do not occur at the precise distance of 90°.So I want to figure out the φ which is φx-φy. ...
63 views

### Doubt from permutation [closed]

Let $Mn=(0.a1.a2....an-1.an)$ be set of fractions such that ai=0 or 1 for i belongs to (1,2,....n-1) and an=1. If Tn and Sn be number and sum of all elements inn Mn then find lim $n \to _\infty$ Tn/Sn ...
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### Are all connected graphs with degree sequence $(2,2,4,4,6)$ Hamiltonian?

Are all connected graphs with degree sequence $(2,2,4,4,6)$ Hamiltonian? I have the following few observations: Note that there are only $5$ vertices but the highest degree is $6$. Hence the graph is ...
21 views

### If asked to use the parity check equations to work out the minimum weight of Code word C. [closed]

So I know that there is 4 independent columns .I am trying to prove that all codewords except 00000000 and 11111111 has a weight of 4.The matrix below is my parity check matrix. I have coded something ...
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1 vote
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### Arrange N unit squares in form of a grid such that number of rectangle is maximum?

You are given N square tiles of dimension 1×1. You have to arrange them in form of a grid such that total number of rectangle (of all possible dimensions) is maximum. Hollows within the grid are not ...
1 vote
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### Why does the method of inclusion/exclusion give the wrong answer when finding the number of integers b/w 1 and 10 that are not divisible by 2,3 or 5?

Let $S=\{1,2,\dots, 10\}$. METHOD 1: I'm first counting the integers that are divisible by $2, 3$ or $5$ in $S$ and then subtracting from the total as follows: Let $A, B, C$ be the set of integers ...