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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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Show that $x-1=0$ has a solution in $\mathbb{N}$ and $x+1=0$ does not have a solution in $\mathbb{N}$

Show that $x-1=0$ has a solution in $\mathbb{N}$. It seems too easy. Just use the induction process? I know $x$ is $1$, which is a natural number. May be that is all we have do that. Also show that $x+1=0$ does not have a solution in…
Lily
  • 395
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Discrete Math - Complements

I'm trying to figure out why the answer would be everything but 0,2,3 as the universal set is 0-9.. I don't know how to explain that the answer would be {1,4,5,6,7,8,9} LETTER G
Robert Miller
  • 317
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newton's binomial

Formulate Newton's binomial's solution and, using that, deduce that this formula is true: $${n\choose 0} + {n\choose 1} + \cdots + {n\choose n-1}+{n\choose n} = 2^n$$ I know that Newton's binomial is $$(a+b)^n={n\choose 0}a^n + {n\choose…
Nerea
  • 21
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Recurrence relation with quadratic equation

Situation: working on a homework problem for my discrete math class that I think is solved, but I am now wondering if my solution is right. This a is a recurrence relations problem with a quadratic equation to find the roots and then an extra term…
user401806
  • 21
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Why is this way used to solve for base 10 to base $16$

In one of my courses there is a problem to convert $142$ base $10$ to base $16$, I know the answer is $8E$ base $16$ just through dividing $142$ by $16$ but the solution is show to use base $2$ like this $2^7+2^3+2^2+2^1=142$ and then in binary…
0101
  • 141
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What is the number of integer solutions of the following equation ? Find the solution without computing 9 combinations.

The equation is: $$x_1+x_2+x_3+x_4+x_5+x_6<10$$ with $x_i\geq 0$ for $i=1,2,\dots,6$. What is the number of integer solutions of the following equation ? Find the solution without computing 9 combinations.
Merve Gürsu
  • 25
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Prove that the number is the product of two successive positive integers

Prove that the number $\underbrace{11\cdots 1}_{100\text{ digits}}\underbrace{22\cdots 2}_{100\text{ digits}}$ is the product of two successive positive integers. What is the general method for this class of proof (big integers)?
user300045
  • 3,449
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Confusion over a question on relations

I've been asked to explain why "a binary relation, $R$, that is irreflexive and transitive will be anti-symmetric." I started to think about the question by coming up with some relations that I understood to be both irreflexive and transitive. One…
paleto-fuera-de-madrid
  • 23
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Decreasing term assurance - find the interest rate

A formula for decreasing term assurance is: $$ V_0 = V_k \times \left(\frac{1-(1+r)^{-n}}{1-(1+r)^{-(n-k)}}\right) $$ where $r$ is the annual rate of interest, $V_0$ is the sum assured at time $t=0$ and $V_k$ is the sum assured at time $t=k$. The…
user2948208
  • 23
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Prove $a^p\equiv a\pmod p$

Prove $a^p\equiv a\pmod p$, $p$ is a prime number. Well, apart from writing this as $ a^p \pmod p = a \pmod p$ I don't know how to continue from here.
Ilan Aizelman WS
  • 4,128
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Evaluate the summation of $(-1)^k$ from $k=0$ to $k=n$

$$\sum_{k=0}^n(-1)^k$$ I know that the answer will be either -1 or 0 depending on whether there are an odd or an even number of sums in total, but how can I determine this if $k$ goes to infinity (which I am thinking means there is neither an even…
user1861051
  • 357
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Find the last digit of $7^{7^{7^7}}$

I was trying to solve this equation but I couldn't find a way to prove that this number ends with a 3 (my teacher has given me the answer). Can someone explain me why? $7^{7^{7^{7}}}$
Dragan Zrilić
  • 637
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Two sets and functions that satisfy the following conditions

I need to come up with two sets and functions called A, B that satisfy three conditions. The two functions are f: A ⇒ B and g: B ⇒ A. The three conditions are: (i) Both functions must be onto. (ii) f(g(x)) = x for all x in B (iii) There exists y in…
AlexK
  • 23
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Find the necessary and sufficient conditions on $a$, $b$ so that $ax^2 + b = 0$ has a real solution.

This question is really confusing me, and I'd love some help but not the answer. :D Is it asking: What values of $a$ and $b$ result in a real solution for the equation $ax^2 + b = 0$? $a = b = 0$ would obviously work, but how does $x$ come into…
Doug Smith
  • 1,015
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If $a$ and $n$ are relatively prime, there is a unique natural number $b < n$ such that $ab \equiv_n 1$

I really don't know how to tackle this proof because it has mod in it. There's 3 parts to the question. You don't have to answer all three parts (would be cool to check answer with though), I just need a starting point so get this proof rolling.…
Krio
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