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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24 views

Graphs Isomorphisms Degrees proof

Can anyone explain what this means maybe in a simple example and show me how to proof this? Would really appreciate it, thanks.
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1answer
49 views

did I solves this sets correctly?

need to solve this only with what we know about 'algebra of sets', is everythink I did is legal and it's correct? i. (A1$\bigcup$A2) $\setminus$ (B1$\bigcap$B2) = (A1 $\setminus$ B1)$\bigcup$(A1 ...
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0answers
40 views

Prove the following sets equalities

I'm really struggling with proofes, please tell me if I'm correct and if there is a better way to prove (or disprove) the following: i) $(A \setminus B) \setminus B = A \setminus B$ My answer: ...
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0answers
20 views

Discrete Math creating functions that map sets

contruct a simple one-to-one function from $Z^+ → P(Z^+)$ How would I approach this type of problem? I'm guessing from utilizing $F: Z^+ → P(Z^+)$ I'm guessing need to find some way to map all ...
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1answer
93 views

Uses of integral calculus in discrete mathematics?

I have to do a project in my integral calculus class. But all the topics are too mainstream (parabolic arc calculation,archimedean approzimation of circle are,obtaining $E=mc^2\dots$ However I'm ...
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5answers
42 views

help solving this proof with remainders

For all $n\ge3\in \mathbb N$, if $n \equiv 3 \pmod{4}$ then ${3^n} \equiv 2 \pmod{5}$. I tried to set $n = 3+4k$ but it doesn't help. Any hints first please?
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3answers
70 views

Discrete Math Testing Cardinality

$S$ denotes the set of real numbers strictly between $0$ and $1$. That is, $S = \{x \in R\mid 0 < x < 1\}$. Let $U = \{x \in R\mid 0 < x < 2\}$. Prove that $S$ and $U$ have the same ...
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0answers
35 views

Prove by induction about line set

A set of straight lines in the plane is said to be in general position if no two lines are parallel and no three lines intersect at a common point. Consider $n\geq3$ lines in general position in the ...
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2answers
148 views

An example of a function whose domain is the set of positive integers and range is the set of integers?

I was browsing through one of my old pre-calc books, and I feel a bit ashamed to say I can't think of a simple answer. It intuitively feels impossible, as there are half as many points in the domain ...
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1answer
138 views

Inclusion and Exclusion Word Problem: Discrete Math

I am having trouble understanding how to solve this question: Some five courses are offered in a semester. The group of students who take at least one of these courses consists of 155 students. ...
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1answer
46 views

Pre requisites of linear algebra

I want to learn abstract linear algebra. Do I require the knowledge of discrete mathematics before I start? I have the impression that abstract maths and their proofs can be understood easily by the ...
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1answer
65 views

What is the Deterministic Traffic Generation Model?

I am studying Markov chains and queuing theory. I was curious about traffic generation models and actually happened to see the Deterministic Traffic Model, referred to as $D$ in Kendall's notation. ...
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2answers
94 views

How many vertices does this tree have?

Suppose that $T$ is a tree. It has $e$ edges and $n$ vertices, and $\overline{T}$ has $10e$ edges. What is n? I think $n = 1$ is a solution, because $T$ can have no edges then, so $0=10*0$. A ...
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2answers
67 views

Prove via induction this recursively defined sequence

Let $P(n) = 2P(n-1) + n, P(1) = 3.$ Use induction to show that $$P(n) = 3(2^n) - n - 2$$ Highly verbose solutions are greatly appreciated.
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1answer
37 views

Queue system with queue-triggered input process

I have a queue system, a classic system with an input generator, a queue and a servant. The servant is a $M$-servant with a certain serving rate $\mu$. The queue can contain an infinite number of ...
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2answers
583 views

Is there a relation that is irreflexive, anti-symmetric and not transitive?

from the set $\{a, b, c, d\}$? Of the one's I have tried, it at best is two of the three, but never all.
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0answers
37 views

are those sets regarding the empty set are true or false?

for X = $\emptyset$ Y = {$\emptyset$ , foo} (foo is an element which is not a set) Z = { $\emptyset$ , {$\emptyset$} } are those sentences true or false? I wrote my answer next to them, please ...
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1answer
35 views

solve a set in 'algerba of sets' way.

two question, need to solve each in 'algebra of sets' way $$(A \cup B) - (C \cap D) = (A - C) \cup (A - D) \cup (B - C) \cup (B - D)$$ $$(A \cup B) \cap (C \cap D)^\complement = (A \cap ...
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1answer
49 views

Applying the Chinese remainder theorem

I am trying to apply the Chinese remainder theorem to obtain the unique solution modulo $10^n$ for $N\equiv 1 \pmod {2^n}$ and $N\equiv 0 \pmod {5^n}$. I have reason to suppose that the solution is ...
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1answer
77 views

Big Oh and Big Theta relations confirmation

I just want to confirm these statements, I know that Big O, and Big theta, are partial order and equivalence relations respectively, all positive integers, but not sure on these restrictions. $f:N ...
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1answer
192 views

combinatorics questions from studying

Hi all I need some assistance How many 5-digit briefcase combinations contain 1.Two pairs of distinct digits and 1 other distinct digit. (e.g 12215) I wasn't sure on which approach was correct. 10 ...
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2answers
87 views

T and F on some discrete math concepts

I was studying and these questions came up on a review guide on the inter webs, but could was wondering if I was correct on them. 1.Let $B$ $\subset$ $A$ and $f$ : $B$ $\subset$ $A$ be a 1-1 and ...
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2answers
88 views

Discrete Mathematics proving set equality

Refer to this Definition to solve the problem bolded: If $f : X \to Y$ is a function and $A \subseteq X$ and $C \subset Y$ , then $f (A) = \{y \in Y\, |\, y = f (x)\text{ for some }x \in A\}$ and ...
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1answer
316 views

“Opposite” of idempotent operation?

What is the adjective given to a mathematical operation/expression on a variable whose new value can only be described in terms of that variable's existing value? Sequential operation? Example: i = ...
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1answer
88 views

How to find multiplicative orders of all elements in field $\Bbb F$ (say $\Bbb F_{13}$)?

I am working on some finite fields and I was referring to some online class material. Is there any way to find the multiplicative orders of all elements in a field $\Bbb F$?
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2answers
82 views

Discrete Maths Logic Question

p = False, q = True and r = False. Is $¬(p∨q)∧(¬p∨r)$ = false? My reasoning: $$(p∨q)=T \text{ as it is (F or T)}$$ but its the negation so $¬(p∨q)=F$? Then, $(¬p∨r)$ as p is F but its the ...
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4answers
66 views

Prove that $a \equiv b \pmod{m_1m_2}\implies a \equiv b \pmod {m_1}$

So, I have this problem: if $$a \equiv b \mod(m_1m_2)$$ then (show) $$a \equiv b \mod(m_1)$$. I have to do a proof, but I have no idea where to begin the proof. Can someone help? Proof (Edit): ...
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1answer
106 views

How to calculate the Lambda of Poisson distribution from mean of inter arrival time?

I have inter arrival time into a system mean equal to$ 0.45.$ Does $\lambda = \frac{1}{0.45}$ if I need to select Poisson as an arrival distribution?
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3answers
61 views

Prove that $3+ 3\cdot5+…+3\cdot5^n = \frac{3(5^{n+1}-1)}{4}$ for all nonnegative integers.

I have been stuck on this one for a while. Supposed to use induction to prove that $3+ 3\cdot5+...+3\cdot5^n = \Large\frac{3(5^{n+1}-1)}{4}$ for all nonegative integers. I don't know if I'm taking ...
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2answers
73 views

How can you infer that $A\cap B = \emptyset$?

Given: $$H:((A \cup B) \to \{ 0,1\} ) \to ((A \to \{ 0,1\} ) \times (B \to \{ 0,1\} ))$$ $$H = \lambda f \in (A \cup B) \to \{ 0,1\} .\left\langle {\lambda a \in A.f(a),\lambda b \in B.f(b)} ...
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1answer
34 views

Prove by Induction (Geometric Progression)

Prove by induction that for any real number $q≠1$ and any $n\in \mathbb N$ we have $ \sum_{i=0}^n q^i=\frac{q^{n+1}-1}{q-1} $
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3answers
136 views

how to prove if $m^{2}|n^{2}$ then m|n just hint please. [duplicate]

How to prove the following?: Let $m,n\in \mathbb{N}$ ; $ \;m^{2}\mid n^{2}\Longrightarrow \;\;m\mid n$ Just a hint please. I tried two ways but did not work.
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3answers
30 views

Negation Syntax Rules

¬(p∨q)∧(p∨r) Does this mean the negation of both (p∨q) and (p∨r) or just ...
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0answers
86 views

Discrete Math, Negation and Proposition

I hope we are all well. I'm having a little hard time understand what negation means in Discrete maths. Say I have "$2+5=19$" this would be a "Proposition" as its false. So how would I write the ...
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0answers
23 views

Discrete Logs and Generators Property

If given some $X$ that is $g^x$ and I want to find $x$ but cannot use $X$ directly does it follow that : $X*g \equiv g^\left(x+1\right)$ $ DLog(X*g) = x+1$ Therefore $x = DLog(X*g) - 1$? I tried ...
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3answers
163 views

Prove that, for any positive integer n: $(a + b)^{n} \leq 2^{n-1}(a^{n}+b^{n})$

Prove that, for any positive integer n: $(a + b)^{n} \leq 2^{n-1}(a^{n}+b^{n}) $ I tried induction theorem, when $n = 1$ it is obviously right. But, say $n=k$, It does not make sense since I cannot ...
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0answers
41 views

How to show that $\sum\limits_{k=0}^{\lfloor0.999n\rfloor}\binom{2n}{k} < \binom{2n}{n} $ holds for large n

It seems logical to me since $\binom{2n}{n}$ is in the middle of the row in pascal triangle; therefore, the largest, and for large n the sum adds only the small ones on the left. But I do not have any ...
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2answers
166 views

Cartesian Product for not a finite number of elements has how many elements

Suppose P is a set that has m elements and Q is a set with n elements. How many elements will their Cartesian product, PxQ have?
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1answer
17 views

Graphs Isomorphisms Degrees

I'm not exactly sure if I'm right but I wanted to double check on how I approached this problem. If its wrong, can you please provide me with hints or suggestions or maybe an answer which an ...
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4answers
53 views

How many different functions $f: A \rightarrow B$ are there if $|A| = m$ and $|B| = n$

I'm not quite sure of what this question is asking. Can someone explain please
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3answers
51 views

Proving equality with floor by contradiction

Prove that if $x\notin Z$ then $\lfloor ax \rfloor \neq a \lfloor x \rfloor$ for some $a \in Z$. I know it can be proven by taking two cases into account: $ax$ being or no being an integer. However, ...
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4answers
84 views

logic: two simple math contradictions

1.The contradiction of the sentence: - There is a greater number than a million. can be stated as follows: - There is a number which is not greater than a million. 2.and the contradiction of the ...
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68 views

Rules of inferences problem

I have a exercise that I have to prove the validity of the following arguments using rules of inferences But there is a exercise I have no idea how to prove it at all. Problem shows as below. P-> ...
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0answers
105 views

General (Set Builder) definition for a relation composed with itself n times

Questions What does the set builder notation for $S\circ R$ look like? I'm having the most trouble knowing when there is too much information or not enough information on either side of the 'such ...
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1answer
79 views

An easy question with integer numbers

I have an easy question of arithmetic. Let $a, b, N$ be integer numbers such that $\mathrm{gcd}(a,b,N) = 1$. Is it true that there exists an integer number $x \in \mathbb{Z}$ such that ...
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1answer
32 views

Number of moves to switch all tiles from black to red?

Four tiles are arranged as per the diagram and all start off black. On each move, two connected tiles may be interchanged, and upon doing so each of the two tiles switches color from red to black ...
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2answers
22 views

Discriminate Maths Equation Understanding

$X = \{x : 3x²−x−2=0\}$ the result is $x=1$ or $x=-\frac{2}{3}$ I must not be reading the question correctly as if $x=1$ wouldn't the question be $X = \{x : 31^2−1−2=0\}$ ? Sorry I am rather new to ...
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1answer
25 views

Checking the equivalence relations of sets

$S=\{0,1,2,3\}, R:SxS, (m,n)\in R \text{ if } m+n=4$. From the condition of $R$, I found that $R=\{(2,2),(1,3),(3,1)\}$. Now I have to see if $R$ is reflexive, symmetric, antisymmetric, and ...
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4answers
135 views

Prove ${k \choose k} + {k + 1 \choose k} + {k + 2 \choose k} + … + {n \choose k} = {n + 1 \choose k+1}$

I have the following problem at discrete maths subject on college. Let's say that $k, n ∈ {0, 1, 2, 3, ...}$ and $k <= n$. Prove the following: ${k \choose k} + {k + 1 \choose k} + {k + 2 \choose ...
4
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1answer
103 views

General approach to puzzles such as the “6 books puzzle”

Six different books (A,B,C,D,E,F) of identical size are stacked as in the figure. We know A and D are not touching. E is between two books which are both vertical or both horizontal. C touches ...