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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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Finding the coefficient in the expansion

I need help finding the coefficient of $x^7y^2$ in the expansion of $(2x-y)^9$ if you could give me a hint
user124557
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Converting to english

I am working on homework right now, and I am not sure of how to solve this problem. I am not sure of how to come up with the translation. Any help is greatly appreciated. This is the problem: Write this in English: ∀k ∈ 3Z ,∃S ⊆ N ,|S | = k…
beginnerprogrammer
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I'm trying to prove there is infinite rational numbers between any two rational number

I understand how to explain but can't put it down on paper. $\displaystyle \frac{a}{b}$ and $\displaystyle \frac{c}{d}$ are rational numbers. For there to be any rational between two numbers I assume $\displaystyle \frac{a}{b} < \frac{c}{d}$. I let…
user3239138
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Discrete Math- Four different dice are rolled

Four different dice are rolled. a) In how many outcomes will at least one five appear? b) In how many outcomes will the highest die be a five? I think i figured out the answer for how many outcomes will the five appear at least once. So what I got…
Roy Kesserwani
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Sigma-notation for summing, relationship between index variable on Sigma sign and variable in summand

In the Sigma-notation the index variable bound to the Sigma sign is said to be unrelated to the appearances of the variable in the summand. For example, in the sum $\Sigma_{k=1}^n a_k$ the subscript $k$ in $a_k$ is said to be not linked to the $k$…
user124485
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Suppose x and y are coprime integers and z is a natural number. Prove that If xy is a zth power then x and y are both zth powers.

I'm supposed to use a prime factorization somewhere, and that the fundamental theorem of arithmetic is to be applied as well.
user122661
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Find the number of integer solutions of the equation $x_{1}+x_{2}+...x_{6}=7, \text{ with } 0 \leq x_{i} \leq 2,i=1,...,6$

Find the number of integer solutions of the equation $ x_{1}+x_{2}+...+x_{6}=7, \text{ with } 0\leq x_{i} \leq 2,i=1,...,6 $ .I found that it has $\binom{12}{7}-5\binom{9}{4} $ solutions..Could you tell me if my result is right?
evinda
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How many hours are needed so that each team has had a meeting?

There are 6 teams $E_{1},E_{2},....,E_{6}$ and each team has to have a meeting to discuss about something. How many hours are needed (minimum) so that all the meetings have been done, when: \begin{align*} E_{1}&=\{A,B,C\} \\ E_{2}&=\{A,D,E\}…
evinda
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Exercise in discrete mathematics

fill in the blanks among 400 persons .... have the same birthday             Answer : At least 2 .... were born on same day of week       Answer : At least 58 ....were born in the same month      Answer : At least 34 But I…
MathDisease
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How much is modulus( 3214020402^43424492897 , 308 )?

Let $$B=3214020402$$ $$E=43424492897$$ $$A=B^E$$ How much is modulus( A , 308 ) ? My try: $$[A]_{308} \to ([B]_4^E,[B]_7^E,[B]_{11}^E) = ([2]_4^E,[5]_7^E,[10]_{11}^E)$$ Applying Eulero-Fermat Rule to each member led me to solve this Chinese…
Angelo Tricarico
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Examples of transitive and not negatively transitive binary relations

Example of a binary relation that is transitive and not negatively transitive: My try: $1\neq 2$ and $2\neq 1$ does not imply $1\neq 1$ Not neg transitive. But if $1=2$ and $2=1$ then $1=1$ by transitivity. Example of a binary relation that is…
OGC
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Discrete Math Set Problem

I came up a problem with for one of the question. I have to proof if the following statement is true/false. $$C\setminus(A\setminus B) = (C\setminus A)\cup(C\cap B)$$ I am a little confuse $C\setminus(A\setminus B)$. I am not sure where to start.…
Big Ticket
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Biconditional Statement

Upon reading my textbook it gives a definition for a biconditional statement as the following: Given statement variables $p$ and $q$, the biconditional of $p$ and $q$ is "$p$ if, and only if, $q$ and is denoted $p \leftrightarrow q$. It then…
iwatakeshi
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Show that $(p \rightarrow q) \land (q \rightarrow r) \rightarrow (p \rightarrow r)$ is a tautology.

Given there are 3 logical variables $p$, $q$ ,$r$. Show that $(p \rightarrow q) \land (q \rightarrow r) \rightarrow (p \rightarrow r)$ is a tautology And here is my steps: $\neg(p\rightarrow q) \land (q\rightarrow r) \lor (p\rightarrow r)$ What…
JAWA
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Applying Fermat's Little Theorem: $6^{1987}$ divided by $37$

Find the remainder when $6^{1987}$ is divided by $37$. Because 37 is prime we have: $6^{36}$ mod $37 = 1$. I tried to get a nice combination like: $1987 = 36 * 55 + 7$, so we would have $(6^{36})^{55}6^{7}=6^{1987}$. Then, I've taken mod $37$, which…
Daniel C
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