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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8 views

How can I find out the Energy of this Energy signal?

I am trying to solve the problems in my text book. but I reached an impasse in 'discrete-signal' chapter. $x[nT]=(-0.5)^nu[nT]$, $ $ $ $ $T=0.01s$ ...
-1
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0answers
26 views

Understanding the set structure of probability theory [on hold]

Since events have their own probabilities and outcomes have their own probabilities. Why don't we just consider only one of events or outcomes directly? What's the motivation to have this set-point ...
-1
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1answer
21 views

What are good techniques for creating a DFA state diagram given a set of accepted/rejected strings?

I am in a Discrete Structures class and my teacher went to MIT so he is pretty big on proving his intellect to the class and getting an average of about 60% for his test questions. Right now we are ...
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1answer
34 views

Need help on understanding a theorem on subsets

An example in my textbook for Discrete Mathematics states, that, Let A be a set, and B = {A, {A}} Then A is a included in B, and so is {A} also an element of B. (Understood) Also it states, {A} is a ...
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2answers
56 views

Is there an application form $\emptyset\to\emptyset$.

What is the cardinal of $\mathcal F(\emptyset,\emptyset)$ where $\mathcal F(X,Y)$ is the set of the function from $X\to Y$ ? I would say $0$ because a function can't associated nothing at nothing, but ...
2
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0answers
21 views

Submodular function, square of which is also submodular?

A Submodular function $ f:2^E \rightarrow R $ is a function that satisfies the following two equivalent definitions: for every $ S,T\subseteq E: f(S) + f(T) \geq f(S\cup T)+f(S\cap T) $ for every $ ...
-1
votes
1answer
65 views

define two functions whose compositions are equal to identity

Let B be the set $B = \{1,2,....n\}$ where n is a positive integer. Let C be the set of all bitstrings of length n and let Z be the set of all functions from B to $\{0,1\}$. How do I find the two ...
14
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13answers
2k views

Show that from a group of seven people whose (integer) ages add up to 332 one can select three people with the total age at least 142. [on hold]

I need help with this problem, and I was thinking in this way: $$ x_{1} + x_{2} + x_{3} + x_{4} + x_{5} + x_{6} + x_{7} = 332 $$ and I need to find three of these which sum is 142. But I don't know ...
2
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2answers
38 views

If $\gcd(ab,c)=d$ and $c|ab$ then $c=d$

For all positive integers $a$, $b$, $c$ and $d$, if $\gcd(ab, c) = d$ and $c | ab$, then $c = d$. Need help proving this question, I know that $abx + cy = d$ for integers $x,y$ and that $c|ab$ can be ...
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1answer
33 views

Raising an adjacency matrix to a power: Why does it work?

An adjacency matrix $M$ represents the number of ways to travel between pairs of points in a network in exactly one move. $M^k$ represents the number of ways to travel between pairs of points in a ...
3
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4answers
57 views

Intuitive explanation for p ∨ q → r ≡ ( p → r) ∧ (q → r)

Although, it is possible to prove the above equivalence using truth tables, I don't know how to prove it without using truth tables.Can someone explain it in plain english?
3
votes
1answer
31 views

How many numbers between 1 and 10000, inclusive, are multiples of 12 or 20?

I calculated the multiples of 12 and multiples of 20, 833 and 500 respectively. Now I calculated the multiples of 12 * 20 = 240,and as a result have 41. The solution would be 833 + 500-41 = 1292 ...
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0answers
22 views

How does an image an preimage come about from inequality? [on hold]

How does an image or a preimage come about from inequality like this: f(x)={1 < x < 4}
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1answer
26 views

uniform distribution vs normal distribution for discount use case [on hold]

Problem statement: Reward a customer with lucky draw coupon of X% discount in between 1% to 100% Assume that slabs are pre-defined ( all are theoretical) 1% discount : 90% customers 10% ...
0
votes
1answer
26 views

Union of subspace

Q. Say U and W are subspaces of a a finite dimensional vector space V (over the field of real numbers). Let S be the set-theoretical union of U and W. Which of the following statements is true: a) ...
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votes
1answer
34 views

Can someone check my answers on group permutation and answer part (g) [on hold]

it would be great if someone could check my answers for Question 5 and answer part (g) Thanks you very much! Question 5: ...
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votes
0answers
37 views

Non repeatable combinations [on hold]

There are 10 girls and 15 boys in class. They're preparing zumba dance for the final show. The teacher decided that boys are doing better and only boys will play 3 zumba dances. Every each of them ...
2
votes
2answers
54 views

How to determine a kind of distance between two permutations?

Let's define a distance between two permutation of length $N$: it is the minimum steps to change one to be another. "A step of change" means that exchanging any two elements' location. For example, ...
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0answers
32 views

Find the extreme points of the below polyhedral sets

Find the extreme points of the below polyhedral sets: (a)$$ P =\{(x_1,x_2,x_3)|x_1 +x_2 +x_3 ≤1,x_1,x_2,x_3 ≥0\}.$$ (b)$$ P = \{(x_1, x_2, x_3 x_4|x_1+ x_2+ 0.5 x_ ≤ 1, x_1 x_2,x_3,x_4≥ 0\}. $$ ...
3
votes
1answer
28 views

If $b \equiv 0 \pmod a$ and $c \equiv 0 \pmod b$, then $c \equiv 0 \pmod a$

The question is If $b \equiv 0 \pmod a$ and $c \equiv 0 \pmod b$, then $c \equiv 0 \pmod a$. My attempt is that $b \equiv 0 \pmod a$ can be written $a\mid b-0 = a\mid b$ and the same with $c \equiv 0 ...
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0answers
27 views

I need a Discrete Mathematics book that breaks down solutions to the Algebraic level to explain how they work. Which one does that? [on hold]

By breaking it down to the Algebraic level, that means they even explain what they're doing Algebraically. I need something where I'm not second-guessing how they did it, or clueless altogether. They ...
0
votes
1answer
26 views

Find number of nonnegative integer solutions to x+3y+3z=n, given n, using generating functions

For every $n,x,y,z\in \mathbb N$, where $x\ge{0}$ and $y,z \ge1$ Find the number of nonnegative integer solutions for $x+3y+3z = n$ I created a generating function for the problem: ...
0
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1answer
48 views

How many different words can be formed using the letters of the word “ PERMUTACION”?

Is there any guide to solve this? Edit: This is what I do. I used the permutations. Please check if I did the right thing? Since 11 words so i did 11Pr 1 letter 11p1 2 letter 11p2 11 3 letter ...
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0answers
21 views

In a special deck of playing card, one which doesnt contain any Jack, Queen or King [on hold]

Determine the probability of the following events: a. Drawing a space (one card) b. Drawing a black card (one card) c. Drawing of four hearts ( four card) d. Drawing of full house (five cards) e. ...
5
votes
4answers
121 views

Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$ [duplicate]

I am studying combinatorics and I came across the identity $$\sum\limits_{k=0}^n \binom kp =\binom {n+1}{p+1}.$$ I have read the algebraic proof and it does not appeal to me. Is there an elegant ...
0
votes
2answers
16 views

Define temperature by clustering with math operators

I can´t figure out how to cluster the temperature for the weather in 3 optimal cases: hot, mild, cold My data contains: air temperature(the average daily value), max air temperature(highest daily ...
14
votes
1answer
1k views

True or false: {{∅}} ⊂ {∅,{∅}}

Note: Actually there's no error in the book and the manual. I actually misread it. The answer is of a different question : True or False: {0} ⊂ {0} This question is from Discrete Math Book by Rosen. ...
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2answers
47 views

Discrete mathematics: Question regarding “Pigeonhole principle”. [on hold]

Each point in the plane is coloured either red or blue. Show that there are two points of the same colour which are exactly 1 cm apart.
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2answers
1k views

Pigeonhole principle: Five points on an orange

Five points are drawn on the surface of an orange. Prove that it is possible to cut the orange in half in such a way that at least four of the points are on the same hemisphere. (Any points lying ...
1
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3answers
62 views

How many ways can 6 cars ( 3 pink, 2 orange and 1 yellow) be parked in 6 parking slots in a row?

a. If the pink cars must be park together? - my answer is 4!3! or 144 b. If the orange cars must not be parked together? c. If you can't park the yellow on either end? d. If a pink car must be on ...
1
vote
3answers
33 views

solve non homogeneous recurrence relation with only '1' as root of its equation [on hold]

I'm stuck in this relation: $f(n) = f(n-1) + 3n - 1$ I've tried to search everywhere if I could find this kind of example where there is only root and that is '1' but all in vain. And all the ...
1
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1answer
64 views

Example to show that $f(A-B)$ is not necessarily a subset of $f(A) - f(B)$

Suppose f : X→Y is a function and A,B ⊆ X. I am trying to come up with counterexample to show $f(A-B)$ is not always a subset of $f(A) - f(B)$ and this is what I have so far: $A = \{1,2,3\}$ $B = ...
-3
votes
1answer
23 views

Is statement “Bitwise Xor of y and y+1=z and y>z” true? [closed]

Can y be greater than z in the condition. Bitwise Xor of y and y+1=z and y>z
0
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0answers
27 views

XOR N and N+1 to get M [closed]

You are given a positive no M and it is required to find a no N, such that N xor N+1 = M N ^ N+1 = M find N How to find it i have tried it a lot... I just cant get any way to solve it except for the ...
-3
votes
1answer
26 views

How to define ordered pairs [closed]

How do we determine the ordered pairs in the relation determined by the Hasse diagram on the set A = {a, b, c, d, e}. And how do we dreate the matrix representation of this poset.
0
votes
2answers
38 views

Diagonalization Principle

Diagonalization principle has been used to prove stuff like set of all real numbers in the interval [0,1] is uncountable. How is this principle used in different areas of maths and computer science ...
0
votes
1answer
52 views

How many 3-digit positive integers can be formed using the digit 0,1,2,3,4 and 5?

No repetition of digits? With repetition? If the integer must be greater than 400? (no repetition) If the integer must be even? If the integer must be odd? If the integer must be divisible by 5? (no ...
0
votes
1answer
39 views

How do I show that if $\gcd(a,b) = d$ then $\gcd(qa,qb) = qd$? [closed]

The question is about greatest common divisor. I have to show that if $\gcd(a,b) = d$ then $\gcd(qa,qb) = qd$.
0
votes
1answer
25 views
1
vote
3answers
72 views

Missing steps: Show the sum of the first n positive integers is of order $n^2$

In Rowsen's Discrete Mathematics text, 6th edition. He has this problem as an example (#11) on page 190. His solution for obtaining a lower bound is to ignore the first half of the terms. He does the ...
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votes
3answers
46 views

Discrete mathematics: How do I solve these three problems? [closed]

1) Use Euclidean algorithm to show that $\gcd (11k + 7, 5k + 3) = 1$ for all values of $k$. 2a) Write $a^4 - b^4$ as a product of three factors. 2b) Show that if $a$ and $b$ are both odd numbers, ...
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0answers
72 views

Does number 1 really exist? [closed]

1) As per decimal system when we start numbering we can start from 0.000000.....1 or the number before 1 ie .99999999999......9 so since .00000... can be infinity we dont even start with the first ...
0
votes
0answers
10 views

Fitness and confidence of discrete function

New to the site, weakly educated in math, and I'm not sure if I'm stating the question in sensible terms (not even sure how to tag it), so I beg your pardon in advance: I'm receiving sequences of ...
-1
votes
2answers
26 views

Mathematics Rubix cube [closed]

In how many ways can rubix cube of 3×3×3 side be solved ? And in how many ways the colours can be arranged on one face of 3×3×3 cube having 6 colours?
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0answers
38 views

Probability question (combination) [closed]

"Solved" - The question is indeed incomplete. In a large company, the executives were surveyed and classified according to their level of education and whether they smoked. The data are shown in the ...
2
votes
2answers
26 views

How many different strings can be made using the letters of ABBCCCDDDDEEEFF such that all the letters D must appear before all of letters F?

There are all together $15$ letters. $1$ A, $2$ B's, $3$ C's, $4$ D's, $3$ E's and $2$ F's. I only know that the total different strings that can be made from those $15$ letters is ...
1
vote
1answer
40 views

Palindrome Remove one Character

We are given a string $S$. If we remove just one character from the string $S$, we can get a palindrome. Suppose $S$ $=$ $aBa$, where $B$ is the middle string, then I need to prove that I can remove ...
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0answers
12 views

Symbolize the following by using quantifiers, predicates, and logical connectives. [closed]

1) All rational numbers are real numbers. 2) Some rational numbers are integers. 3) some even numbers are multiple of two, four, or five. 4) some triangles are scalene. 5) Every integer is multiple of ...
1
vote
1answer
37 views

Induction Proof - Primes and Euclid's Lemma

I'm having some trouble with this proof. Here's the question: Use mathematical induction and Euclid's Lemma to prove that for all positive integers $s$, if $p$ and $q_1, q_2, \dotsc, q_s$ are prime ...
0
votes
1answer
45 views

Combinatorics & Cupcakes

There are $10$ cupcakes left over after a birthday party: $3$ vanilla, $2$ red velvet, and $5$ chocolate. Each of the $8$ guests can take home as many of the cupcakes as they want. How many ways can ...