Mathematics Stack Exchange
Mathematics Stack Exchange

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.

Discrete mathematics is not the name of a branch of mathematics, like number theory, algebra, calculus, etc. Rather, it's a description of a set of branches of math that all have in common the feature that they are "discrete" rather than "continuous".

The term "discrete mathematics" is therefore used in contrast with "continuous mathematics," which is the branch of mathematics dealing with objects that can vary smoothly (and which includes, for example, calculus). Whereas discrete objects can often be characterized by integers, continuous objects require real numbers.

Though there cannot be a definite number of branches of Discrete Mathematics, the following topics are almost always covered in any study regarding this matter −

  • Sets, Relations and Functions
  • Mathematical Logic
  • Group theory
  • Counting Theory
  • Probability
  • Mathematical Induction and Recurrence Relations
  • Graph Theory
  • Trees
  • Boolean Algebra

For an overview, see the Wikipedia entry on Discrete mathematics.

and http://www.cs.yale.edu/homes/aspnes/classes/202/notes.pdf

Consider using a more specific tag instead, such as: , , , , , , , , etc.

32903 questions
2
votes
7 answers

If I know that $b$ is a multiple of $32$ then how can i show that $b+5$ and $b^2 + 7$ are coprime?

I'm using the polynomial division method and i got a remainder of 32 but how do I explain in words or mathematically how this justifies my solution. The previous question has answers based on Properties of Divisibility but I want to know how I can…
Angela
  • 21
2
votes
1 answer

Suppose $f : \Bbb R →\Bbb R$ where $f(x) = \lfloor x/2 \rfloor$

could someone please explain me how they got this answer ? im trying to figure out
Agape Twentyone
  • 113
  • 6
2
votes
2 answers

Average product of the digits in a car's licence plate

A car's licence plate is on the form $$\underbrace{A...A}_{k\,\text{letters}} \quad \underbrace{19\ldots9}_{n\,\text{digits}}$$ What is the average product of the digits in a car number with $n$ digits? Note: the digits in a licence plate…
N3buchadnezzar
  • 10,896
2
votes
2 answers

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 be shown that - $B$ has infinite number of upper and lower…
user 493905
  • 35
  • 1
  • 17
2
votes
1 answer

Determine whether the following expression is a tautology, a contingency, or a contradiction by using the logical equivalences

As a practice problem, I'm asked to determine whether the following proposition is a tautology, contradiction, or contingency through the use of logical equivalences. I get how to determine what truth value the proposition is and I understand most…
GilmoreGirling
  • 305
  • 1
  • 7
2
votes
2 answers

Determining and justifying the validity of an argument

Context: Question made up by uni lecturer Original statement: There exists two positive real numbers $x$ and $y$ such that for all positive integers $z$, $\frac{x}{y}>z$. So the question was to find the negation of the statement, and then determine…
Ruby Pa
  • 349
  • 1
  • 11
2
votes
1 answer

Why the cardinality of the two sets are equal?

Problem. Consider the set $X=\{0,1,2,3\}$ List all subsets of $X$ which are disjoint from $\{0,1\}$. List all subsets of $X$ which have $\{0,1\}$ as a subset. How many subsets did you find in the previous two parts? What do you notice? Can you…
user656433
2
votes
1 answer

Cascading Summation $\sum_{i_1=1}^n \sum_{i_2=i_1}^n \sum_{i_3=i_2}^n.... \sum_{i_{p-1}=i_{p-2}}^n \sum_{i_{p}=i_{p-1}}^n f(i_p)$

Is there relation between the two summations $$\sum_{i_1=1}^n \sum_{i_2=i_1}^n \sum_{i_3=i_2}^n.... \sum_{i_{p-1}=i_{p-2}}^n \sum_{i_{p}=i_{p-1}}^n f(i_p)$$ and $$\sum_{i_1=1}^n \sum_{i_2=1}^{i_1} \sum_{i_3=1}^{i_2}....…
R. FARKOUS
  • 21
2
votes
2 answers

Construct a permutation of the set N of all natural numbers that maps all the multiples of 3 onto the set of all even numbers.

Question: Construct a permutation of the set N of all natural numbers that maps all the multiples of 3 onto the set of all even numbers. I am confused as to how to get started on the problem. I have tried creating multiple mappings that map…
Captain Kray
  • 45
2
votes
2 answers

I was asked this question in an interview...

If I have a $10 \times 10$ sided cube (rubik's cube is $3 \times 3$ sided), and dropped it in a bucket of black paint, can you tell me mathematically how I could determine the total number of sides that are black?
Chris Olszewski
  • 131
2
votes
4 answers

How do I determine if this relation is an equivalence relation?

I'm trying to do the following problem in my book, but I don't understand how the book got their answer. The problem: Determine whether the following relations are equivalence relations:$\newcommand{\relR}{\mathrel{R}}$ The relation $\relR$ on…
SirChryse
  • 51
2
votes
1 answer

show that the number $n = 11$ is not a sum of $4$'s and $5$'s

I don't know how to get started with this question. $11 = 4(x) + 5(y)$ What I've tried is : $x = 0, y = 2$ $11 = 4(0) + 5(2)$ $11 = 10$ $11$ is not equal to $10$. Wouldn't that be my base case? What more could I do to solve this question? If i…
MathNoob
  • 91
2
votes
2 answers

If then, sufficient for, necessary condition

How could I understand If p then q = q is necessary for p = p is sufficient for q ??? I am so confused why are they the same.
Andes Lam
  • 354
2
votes
3 answers

How can a relation be both not symmetric and not antisymetric?

I am aware that relations can be both symmetric and antisymmetric, or either one of the two. However, I am still a little bit confused as to why they can not be both (i.e. not symmetric and not antisymmetric)?
Bandolero
  • 49
2
votes
2 answers

Solve recursion

$a_n=n^2\times a_{(n-1)}$, for $ n>0, a_0=1$ Whats the correct formula to use in this case? I solved problem with recursion before, but they had '$+$' instead of $'\times'$ so there is following formula to simply solve them: $ar^n+bnr^n$. Is…
Gorosso
  • 85
1 2 3
…
99 100