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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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Proof involving the infinite number of primes

Given that $R = p_1p_2\cdots p_n + 1$ where $p_1 < p_2 < \cdots < p_n$ and $p$ are prime numbers. Prove that if $R$ is not prime then $R$ must have a prime factor $q$ that is larger than $p_n$. I directly understand that this question refers to…
A A
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Three Fundamental Principles

How many different pizzas can be ordered if a pizza can be selected with any combination of the following ingredients: anchovies, ham, mushrooms, olives, onion, pepperoni, and sausage? Can someone give me a hint to this question.
user124557
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Why is a statement such as, "It's 5 o'clock" excluded from propositions?

From MIT notes: A proposition excludes statements whose truth varies with circumstance such as, “It’s five o’clock”. And: A predicate is a proposition whose truth depends on the value of one or more variables. If a proposition excludes…
user87870
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Elevator Problem (Sample Space)

Carefully describe the events $A$, $B$, $A\cup B$, and $A\cap B$ in the following sample space: Six people enter the elevator in the basement of a building with 6 floors. Each states where they will get out. $A$ = {all six get off on the same…
petrov
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,How to show that a set is empty?

How can one show that a set is empty? For example, let the set $A = \{1,2,3\}$ and let the set $B = \{4,5,6\}$. I want to show that $A \cap B = \emptyset$. I know that the typical approach to showing set equality would be, for this case, to show…
Lucas Alanis
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Discrete Math, Difference between $\mathbb Z$ and $\mathbb R$ notation

This may sounds stupid, but in the text book, they ask me a question that is something like this Define $f:\mathbb{R} \to \mathbb{R}$ by $f(x)= 3x + 2$ and $h: \mathbb{Z} \to \mathbb{Z}$ by $h(n) = 3n+2$. a) Is f surjective? Prove or give a counter…
Big Ticket
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Prove that $\frac{1}{1*3}+\frac{1}{3*5}+\frac{1}{5*7}+...+\frac{1}{(2n-1)(2n+1)}=\frac{n}{2n+1}$

Trying to prove that above stated question for $n \geq 1$. A hint given is that you should use $\frac{1}{(2k-1)(2k+1)}=\frac{1}{2}(\frac{1}{2k-1}-\frac{1}{2k+1})$. Using this, I think I reduced it to…
Azovax
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Quantifiers and English: Existential and Universal difference

Firstly, excuse my simplicity in describing the title; I couldn't find a proper title that could explain what I am confused about. The example looks at how we express the following statements in predicates and quantifiers, “Every student in this…
John
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Prove by induction $6\cdot 7^n -2\cdot 3^n$ is divisible by $4$ for $n\ge 1$

Prove by induction $6\cdot 7^n -2\cdot 3^n$ is divisible by $4$ for $n\ge 1$. I am struggling on this problem very much. So far I have Basis case = $6\cdot 7^1 - 2\cdot3^1 = 36$ which is divisible by $4$ Assume for a $n$ that $6\cdot 7^n-2\cdot3^n$…
Jack
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Discrete math library homework

I am working on a homework question and I am not sure if I am going about the correct way of getting to the correct answer. I feel as this is a trick question. Here is the question: In order to keep track of circulation numbers, the library asks you…
beginnerprogrammer
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one-to-one functions question

Let $A$ be a set of size $m$, let $B$ be a set of size $n$, and assume that $n \geq m \geq 1$. How many functions $f : A \rightarrow B$ are there that are ${not}$ one-to-one? Justify your answer.
fdsadasf
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Mathematical Induction of $\frac{n(n-1)(n-2)}{6}$

Show that the number of triples that can be chosen from $n$ items is precisely $$\frac{n(n−1)(n−2)}{6}.$$ Suppose n = k+1, We want $\frac{(k+1)k(k-1)}{6}$ therfore, $\frac{k(k-1)(k-2)}{6}$ + (k+1) and then solve the rest. What am I doing wrong…
Mark
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Divide and Count

I have question that I can't understand it and I don't know how should I solve it. here is the whole question: Jack has several beautiful diamonds, each of them is unique thus precious. To keep them safe, he wants to divide and store them in…
Danial
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Find the remainder when the number $52^{1989}$ is divided by 7.

Find the remainder when the number $52^{1989}$ is divided by 7. I tried arithmetic modular, but seems didn't work
SSS
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Proof of $\sum_{i=1}^{k}(2i-1) = k^2$ and some general questions

My vocabulary in math is lacking quite a lot, so please forgive me if my question is not sufficiently accurate or needlessly verbose. I tried very hard to get the latex flowing, at least that's one thing I got going. In the syllabus from which I'm…
Chris B.
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