# Tagged Questions

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.

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### Linear Travelling Tournament Problem: 4 teams

The linear travelling tournament (LD-TTP) is a variant of the travelling salesman problem (TS). The LD-TTP’s objective is to find a round-robin schedule that minimizes the total travel distance ...
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### What type of order is $A/{\sim}$ if $A$ is…

I find it hard to understand this question and proving different types of order. I hope someone can help me. If $A = \langle A,\ge\rangle$ and for all $a,b \in A$ it’s the case that $a \sim b$ ...
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### Given the function $f:[0,1]→[0,1]$; $f(x)=x^2$, check which one(s) of the properties it has.

This homework is past due, but I am still fiddling trying to figure this out. question: I do not understand what the heck the notation of $f:[0,1] \to [0,1]$; means. I thought I did, but my ...
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### b) How many onto functions are there from A to C? [duplicate]

Let $A=\{1,2,3,4\}$ Let $B= \{a,b\}$ Let $C= \{ \text{hiking, baseball, hockey} \}$ a) How many onto functions from A to B $(1,a) (1,b) (2,a) (2,b) (3,a) (3,b) (4,a) (4,b)$ Thus 8. b) How many ...
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### Clarification on inductive proof of Bernoulli's inequality

Prove that if $h > -1$, then $1 + nh ≤ (1+h^n)$ for all nonnegative integers $n$. I've read several solutions and I'm still totally lost on how to go about this. I have the inductive hypothesis:...
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### Reflexive, Symmetric, Transitive for (a,b)E R iif (a-b) is a multiple of k

If k is any positive integer, and R is a relation on the set 0,1,2,3 as (a,b) are elements of R iif (a-b) is a multiple of k. Is R reflexive, symmetric and/or transitive. I know reflexive means x=x; ...
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### How to prove that partial order is isomorphic a linear order

I'm trying to solve a question in discrete mathematics, but I do not understand how to solve it... The question: Is a partial order (set with four elements) isomorphic a linear order with three ...
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### Hasse Diagram with “better than” relation [closed]

Adam have five elements to choose between; a, b, c, d and e. His preferences (better than) are as follows: a < b b < c c > d a < c b > a c > e a < d b > e a > e Kate have also five ...
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### Consider the system S which can take n input parameters and each parameter can take on m values

(a) What is the maximum number of pairs a single test case for this system can cover? "I know that there are m^n different combinations in this example, but i'm unsure how many pairs a single test ...
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### Order relations and properties, dilemma [closed]

A, B, C and D are prices in a gameshow that I've just won. I must choose one price and according to the task my preferences are; A is equal to C D is equal to A B is equal to C D is better then C B ...
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### How to prove this using laws? [closed]

How do they prove this? $$(p\to q)\land[\neg q\land(r\lor\neg q)]\equiv\neg q\land\neg p$$
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### Number of ways to connect vertices of n squares with line segments

What is the number of ways to connect the vertices of n squares with non-intersecting line segments ? These line segments should not cross the edges of the given squares as well. Obviously $N(3)$ is ...
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### matrix multiplication result value range

Here is the initial question: About the output value range of LeGall 5/3 wavelet Today I found actually the transform can be seen as a matrix multiplication. It is easy to calculate the wavelet ...
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### How to make check matrix H when you have generator matrix (algorithm)

It's all built on top of python numpy lib. So we have a class finite field and get access to elements of field like Finite_field[index_of_element]. Elements of field are numpy matrices(ndarray). For a ...
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### Difference sets without squares of Integers

I am trying to print numbers occuring in A030193 i.e Let S = set of square numbers; a(0)=0; a(n) = smallest m such that m - a(i) is not in S for all i < n. but I am unable to do it in better ...
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### Is $\emptyset$ considered as a powerset by itself?

For example, $X = \{\emptyset, a, \{b\}\}$. Find the power set of $X$. As far as I believe everyone understand, a power set of something means to display whatever element is within the set itself. ...
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### Why am I under-counting when calculating the probability of a full house?

I was trying to answer this question. Find the probability of getting a full house from a $52$ card deck. That is, find the probability of picking a pair of cards with the same rank (face value), ...
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### Is there a basis which spans the real numbers?

Is there a finite set of real numbers $S=\{a_1, a_2, ..., a_n \}$ such that every real number can be written as a linear combination (with integer coefficients) of the elements of $S$? If no, is there ...
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### Why is $\{\{1\}\}$ not equal to $\{1,\{1\}\}$?

Determine whether each of these pairs of sets are equal$$A = \{\{1\}\} \qquad \qquad B = \{1, \{1\}\}$$ I believe $A$ is equal to $B$ because all elements in $A$ are in $B$, but the answer says that ...