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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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Where does $\mathsf{DEBABE}$ appear in a Krilandic dictionary?

The Krilandic language over the alphabet $\Sigma = \{ \mathsf{A,B,C,D,E} \} $ consists of all $6$-letter words without a letter repeating twice successively. In what place does the word $\mathsf{DEBABE}$ appear in a Krilandic dictionary (listing…
Tony Erwin
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How to compute distance in discrete uniform grid?

I am a comp.sci. and am not sure if there is a more efficient way to to this: given a discreet uniform grid, compute distance between grid points, right now I do it with the pyth. thm. is there any other way since this is a discrete and uniform…
mihajlv
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Proofs question

I have a question about set theory that and proofs that I was hoping you could help with. The goal is the prove or disprove that: $A\setminus (A \cap B) = A\setminus B$ So far I have: $A\setminus (A \cap B)$ is equivalent to $A \cap (A \cap…
user1122429
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Proving by contradiction odd values

I need to prove the following by contradiction: "$$ and $$ are odd integers, then $$ is odd" I'm sure this question isn't very hard to solve, however, my understanding of contraposition is very weak. I have only learned it recently and I do not feel…
777
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How to find the set X?

I am given $2$ sets $A$ and $B$ : $A = \{1,2,5,6,7\}, B=\{0,4,6,7,9\}$ and two more sets $C = \{0,1,2,6,7,9\}$ and $M = \{0,1,2,3,4,5,6,7,8,9\}$. I have the following set equation to be solved: $(A \cap X) \cup (B \cap X^c) = C$ My own thoughts have…
mire12
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Minimal and Maximal terms in $A=\{1,2,3,4\}$ and $R$ relation on $\mathcal{P}(A)$

I have the set $A=\{1,2,3,4\}$ and my relation is on $\mathcal{P}(A)$ where $X\subseteq Y \wedge XRY$ I wrote $\mathcal{P}(A)$ and get $$\mathcal{P}(A)…
Ofir Attia
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Partially ordered set question

R is relation over the set of functions continuous in $[0,1]$ that defined $$fRg \Longleftrightarrow f(x) \leq g(x) \rightarrow x\in [0,1]$$ I know that to prove it I need to show that if for all $a \in A$(the functions set) implies $(a,a)\in R…
Ofir Attia
  • 3,136
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5 answers

Prove that $(a,b)R(c,d) \longleftrightarrow ad=bc $ is equivalence relation on $A=R^2-\{(0,0)\}$

I am trying to prove that $$(a,b)R(c,d) \longleftrightarrow ad=bc $$ is equivalence relation on $$A=\mathbb{R}^2-\{(0,0)\}$$ $A$ is all points on the plane. If I want to show that is reflexivity so I need to take $a$ and $c$, set $(a,a)\in R$ and…
Ofir Attia
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Infer a set from its differences to other sets

There is a set $S$. We don't know the exact elements of $S$, but only know its cardinality $|S|$. Now we have some guesses to $S$, i.e., $\{ S_i \}_{i=1}^n$. For each $S_i$, we know its exact elements, and the cardinalities $|S_i \backslash S|$ and…
graphitump
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What are the proper steps needed to solve a prove question?

I was just wondering is there any particular structure of steps you take to solve a question about proof. For eg, For each pair of real numbers x and y, if x + y is irrational, then x is irrational and y is irrational. Since this question is…
CalvinChua
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How to best characterize a monotonic real valued function defined on a power set?

The question is pretty vague because it arises from an application scenario and is open-ended. $\mathcal{S}$ is a countable infinite set, $f$ is a function defined on the power set of $\mathcal{S}$, mapping any subset of $\mathcal{S}$ to a real…
David M
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Hard? problem with the largest square

Let me start by saying that this post is not likely to be a question. I am writing it because I found a mathematical problem that I found interesting enough to share with others. It seems to me that it is rather difficult and thus I rather not…
Mat196
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Let R = $\{1, a\}$, S = $2^R$ and $T = 2^S$. List all the elements of S and T

I am having a little difficulty understanding how to approach this question. When S = $2^R$ and T = $2^S$, would that mean that the elements of S = $\{2^1,\space 2^a\}$ and T = $\{2^2,\space 2^{2a}\}$? By that understanding, would $|S| = 2$, $|T| =…
MH10
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set theory: $A = \{3r+5s+8t \mid r,s,t \in\mathbb N, r = s + t\}$ and $C = \{n \in\mathbb N\mid 0 \le \le 12\}$. Find $A\cap C$

Can someone kindly explain this question to me, I am not sure how to do this. My approach: Since for Set $A = (r = S + T)$ $A = \{ 8s + 11t\mid s,t \in\mathbb N\}$ $C = \{0,1,2,3,4,5,6,7,8,9,10,11,12\}$ based on the interception of these two sets,…
Roses
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