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
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Convert form English to logical symbols.

I have a logical argument in English which says. All Humans are Mortal. Zeus is not Mortal. therefore Zeus is not Human. And I tried to convert it from English to logic. and did this h = is Human, z = is Zeus, m = is Mortal         h $…
Danish ALI
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How many password combination?

How many password combinations if you can have up to 8 letters, uppercase or lowercase, with only letters and no numbers or special characters? My attempt: $$52+52^2+52^3+52^4+52^5+52^6+52^7+52^8$$ because there are 52 possible at each place and you…
bodygued
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Determining number of solutions to equation (Discrete math)

How many solutions are there to the equation below, if $x_i$ is a positive integer > 1: $$\sum_{1}^{6} x_i = 29$$ I also have to do this for x1<=5, however I imagine that's a similar process. So, my question is based on $x_i>1$. Where is a good…
user143918
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Looking for a generalised or non-iterative maths equation for the process of slicing up a range value

Suppose I have a integer range $[0,n]$ and an integer $x$ within that range. Suppose I can generate an integer $y$ though this iterative process: $x$ is converted to Base 2 For each bit from most to least significant: If 0 then cut the current…
LateralFractal
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Discrete Mathematics Riddle, square grid problem

I've been trying to solve this problem in my book to no avail: I am even stuck on part a... to find a closed form of this I started with size 2x2 square, counted the number of paths, then used a 3x3 square, did the same but I feel that was a…
user3367265
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Prove Arrow's Theorem is not true when there are two candidates

I'm trying to prove the Arrow's Theorem is not true when there are two candidates, however I'm having trouble trying to prove that there is no dictator. I have suggested that in a majority rules voting system, unanimity and IIA are satisfied but I…
user2980566
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Prove that at least three students are registered for all four courses

Out of 40 incoming freshmen, 25 are registered for CS 110, 30 are registered for CS 160, 35 are registered for Math 254, and 33 are registered for Econ 101. Prove that at least three students are registered for all four courses.
user3434743
  • 393
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Discrete Math -- Sets

I am struggling with thinking about this. Any help would be great!! A medical research survey categorizes adults as follows: by gender (male or female) by age group (age groups are 18-25, 26-35, 36-50, 51+) by income (less than 30k/year,…
user3320746
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8 men and 8 women in a circle

There are 8 men and 8 women sitting in a circle. Prove that there are 8 adjacent people, so that 4 of them are men and 4 are women. (This is obvious, but how do I prove it?)
user176791
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Number of Elements Not divisble by 3 or 5 or 7

if A={1,2,...,600} includes all natural numbers between 1 to 600. I want to find number of elements of A that not divisible by 3 or 5 or 7? any hint or idea?
Davied Zuhraph
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Can someone explain this proof by case example?

I don't fully understand this example the book gives. I understand the section where they examine when $x\gt0$ but when $x\lt0$ things get murky for me. Prove that for every real number $x$, $x\le\lvert x \rvert$.
secondubly
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Minimum and Maximum of a set

I need help at the following: How can we find the minimum and the maximum of a set of $N$ numbers using $1.5N $ comparisons?
user175343
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4 answers

Proof: For all integers $x$ and $y$, if $x^2+ y^2= 0$ then $x =0$ and $y =0$

I need help proving the following statement: For all integers $x$ and $y$, if $x^2+ y^2= 0$ then $x =0$ and $y =0$ The statement is true, I just need to know the thought process, or a lead in the right direction. I think I might have to use a…
Rienman
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Need help solving a Venn Diagram

I am trying to figure out how to solve this Venn diagram problem for my Discrete Mathematics class. So the problem goes like this: In a school there are 420 students. 300 of them have gone to school by car, 80 of them walking, 120 on a bicycle, 46…
drleifz
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Evaluating equivalence between congruence mod k and congruence mod j

Suppose we know that $$a \equiv b (mod \ k)$$, what must be true for $$a \equiv b (mod \ j)$$ So far this is what I have: We know that these two equivalences can be rewritten as : $$k |(a-b)$$ and $$j | (a-b)$$ Thus we can say that $$kn = (a-b)$$…
Pandamonium
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