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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Erdos Szekeres, combinatorics monotone sequences

Given a sequence S with 21 different numbers. It is known that there isn't any monotone sub sequence in the length of 6. Prove that there exists 2 monotone sequence, one decreasing and the other ...
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3answers
21 views

Combinatorics question about picking a staff

This is the Question : In a building there are 5 men and 5 women. we need to pick representive for the building so that at least one woman and at least one man has to be there. there are no limitions ...
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1answer
20 views

Counting relations question

I have a small question about relation counting, i'm looking for formulas. I know that there is a formula for reflexive and anti reflexive. I'm not sure about the simetric or a-simteric ones, and if ...
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1answer
16 views

$\land,\lor$ and $\lnot$ determinate a functionally complete basis

I read that a Boolean algebra is defined by the binary operations $\land$ and $\lor$ and the unary operation $\lnot$ on a set such that $$\varphi\land(\psi\land \chi)=(\varphi\land \psi)\land ...
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15 views

Importance Sampling of 2D constant piecewise function convertible to 1D?

So I have a constant piecewise 2D function (luminance values of pixels of an image) that I am writing an importance sampling algorithm for. I was going to write my algorithm by first sampling the 1D ...
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1answer
20 views

I have this circuit and I need to use boolean laws to simplify this circuit

I need to use boolean laws to simplify the following circuits need to simplify this so that they contain at least amount of gates: a) (A+B)(C+D)+(A+B)(C'+D')= what I did for a) ...
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1answer
89 views

Am I solving this question correctly?

How can I evaluate the following term: $$\left((\{a,b\}\cup\{b,a\})\times(\{b,a\}\cap\{a,b\})\right)\setminus \left((\{b,a\}\setminus\{a,b\})\cup(\{a,b\}\times\{b,a\})\right)$$ You can see the notes ...
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21 views

Am I doing the Cartesian product of sets correctly?

Question in the image and how I attempt to solve it. Did I do it correctly? And is that the right answer?
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45 views

Proving that $x’y’ + yz’ + x’z’ = yz’ + x’y’$ using the laws of Boolean algebra. [on hold]

I'm trying to prove the following identity using the laws of Boolean algebra. $$x’y’ + yz’ + x’z’ = yz’ + x’y’$$ Here's what I've tried: [insert attempt here]
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21 views

Clique cycles structure

I am currently going through the paper "Covering two-edge-coloured complete graphs with two disjoint monochromatic cycles" by Peter Allen (http://www.ime.usp.br/~allen/twocycle.pdf) and I have some ...
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1answer
14 views

The drawer has M different colored socks. What is the least amount of socks I that I need to draw to guarntee N pairs

So in my discrete math class, we all know that if the drawer has 2 different colored socks, you need to pull out 3 socks to ensure a pair. However, I am puzzled after there are more different ...
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1answer
41 views

What does it mean for a function to be $\Omega(1)$?

I am having a lot of trouble understanding this. Could someone put this in a context I might understand?
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3answers
40 views

Arranging a word

This is the question : In how many ways you can arrange the word AAABBCDEFG so that the first letter is A or E ? I'm not sure if im doing this right. My plan is to take all the arrangments and ...
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1answer
24 views

Diving students into teams

So this is the question : Count the number of ways in which you can divide a group of 33 sudents into 3 soccer teams (each team has 11 studends, them have no names). I know that i shouldn't use the ...
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0answers
3 views

Multinomial Coefficients proof?

prove that if n and m are positive integers, then ∑ (n )*(−1)^(k2+k4+...+k2l) (k1,...,km) k1+...+km is equal to 0 if m =2l, and is equal to 1 if m = 2l + 1. Please ...
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1answer
45 views

Theory of definitions

I am reading "Introduction to Logic" by P Suppes at the moment. In the Chapter 8 - Theory of definitions of it, I 've some confusion, actually about the Conditional Definition. The brief explanation ...
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0answers
14 views

Proving a Recurrence Using Substitution

I am trying to understand an example of solving a recurrence using substitution (or unrolling it) in my book right now, but all of the steps do not seem clear to me. Here is the basic example: ...
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2answers
32 views

Discrete maths proving a random observation

Suppose you had 6 points. Each point can choose to either visit another point, or choose not to visit another point. However, it can't visit itself. In addition, visiting another point works in both ...
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2answers
50 views

How to get to $5^3 \geq n^3$ in the proof by contradiction?

This is the same problem asked here. - Next step to take to reach the contradiction? Here is it again. I understand the solution - how you want to get to the fact 100 divides n^2 and then go ...
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2answers
33 views

how to prove boolean identities

I'm working on 2 boolean proofs (¬p⊕q)=(p⊕¬q=¬(p⊕q) <- I assume its equality law i'm not sure how to do this problem(I verified using truth table but I need to do algebraically) ...
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0answers
19 views

Find all points on the line 9x-21y=6

For this equation we are suppose to use the Euclidean Algorithm. But I run into a problem For the GCD (9,-21)= i tried 9=(-21)(0)+9 -21=9(3)+6 9=6(1)+3 6=3(2) +0 which gives a gcd of 3 and the ...
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1answer
23 views

What is the probability that 13 cards drawn from a standard deck has at least one card from each suit?

I am currently trying to figure out why my answer is not correct for that following question. Q: What is the probability that 13 cards drawn from a standard deck has at least one card from each suit? ...
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1answer
29 views

standard deck and the probability of at least one card,exactly one void and two voids

The question is this: if 13 cards are dealt from a standard deck of 52, what is the probability that these 13 cards include a)at least 1 card from each suit b) exactly 1 void(e.g no clubs)? ...
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1answer
20 views

How can I add the following 32-bit IEEE floating-point numbers?

How can I add the following two 32-bit IEEE floating-point numbers in binary? FEDCBA98(base 16) + 89ABCDEF(base 16) = a 33-bit binary number. How can this be possible?
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1answer
15 views

How would you convert the following 32-bit IEEE floating-point to decimal form?

I have got -1.101 1100 1011 1010 1001 1000 * 2^(9) How can I convert this to decimal form?
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1answer
25 views

Convert the following decimal number into 32-bit IEEE floating-point form.

I am given a negative decimal -1234.875. I understand the normal process of solving a question like this, except I am uncertain about handling the negative. What I do is find the binary form of 1234 ...
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0answers
42 views

Let a1,a2,…,an be real numbers satisfying ai ≥ 1 (for i = 1,2,…,n). [on hold]

Let $a_1,a_2,\ldots,a_n$ be real numbers satisfying $a_i\ge 1$ (for $i = 1,2,\ldots,n$). We want to choose as many partial sums of $a_i$’s, i.e., expressions of the form $a_{i_1} +\dots+a_{i_k}$, ...
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1answer
23 views

How many ways can you choose 4 non empty subsets from q 10 element set

How many ways can you divide the set $A=\{1,2,3,4,5,6,7,8,9,10\}$ into a 4 non empty subsets? Hint: there's a formula states that the number of all the functions from $A \to \{1,2,3,4\}$ that are ...
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1answer
44 views

How many bit strings oft length k have more than one 1?

The question seems rather simple, but I am not able to get a closed formula. e.g. for k=2 it is 1 (11), for k=3 it is 4 (111,101,110,011) I thought that it maybe could be $\frac{1}{2} \cdot 2^k $ ...
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0answers
17 views

How to prove the two relations to be equal?

If I have a relation $R$ defined on a set $A$ ,then when we calculate $R^n$ by performing cartesian product of $A^n$ ,then can we predict the value of $s$ and $t$ such that $R ^ s=R ^ t$. As we ...
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2answers
46 views

Show that there exists no integer $x$ such that $3x$ is congruent to 5 (modulo 6)

So far my approach was to rewrite the congruency to $5-3x=6t$ for some integer $t$. My problem is I get stuck in trying to show how $5-3x$ is never divisible by $6$.
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1answer
25 views

simple diving question in combinatorics

So the Discrete Math exam is on friday and i am still very confused with which formula should i was in cases that looks very simillar, there are these 4 question : a) Divide 30 students to 6 ...
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0answers
40 views

Placing $4n$ non-attaking queens of in a $4n \times 4n$ chessboard.

Is it possible to place $4n$ non-attaking queens of in a $4n \times 4n$ chessboard?? I have found that it can be done for $4 \times 4$ chess board and trying to extend it to $8 \times 8$ chessboard ...
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2answers
42 views

Prove that $f$ is NOT surjective

Let $f: Z \times Z \to Z \times Z$ defined like this: $f(x,y) = (x+y, x-y)$ Prove that $f$ is injective, and not surjective. For injectivity I did that: Let $(a,b) \in Z\times Z$ and $(c,d) \in ...
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2answers
35 views

If $|B\times A| = 15$ ,evaluate: $|A\cap B|$

If $|B\times A| = 15$ and $|A\times B \backslash B \times B| = 12$. Evaluate: $|A\cap B|$ I tried for myself and got to the conclusion that $|A\times B \cap B \times B| = 3 $ I couldn't get by ...
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1answer
17 views

For the following number, state the base represented as t?

$1011 \textrm{(base }t) = 4931 \textrm{(base 10)}$ I have to find $t$, which is the base of 1011. I do the following: $4931 \textrm{(base 10)} = 4 \times 10^3 + 9 \times 10^2 + 3 \times 10^1 + 1 ...
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1answer
84 views

let s be a set with N elements and A1,…,A101 be 101 (possibly not disjoint) subsets of S

So the question I'm having problem with is the following: let s be a set with N elements and A1,...,A101 be 101 (possibly not disjoint) subsets of S with the following 5 properties: each elements ...
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1answer
89 views

How many lattice paths with step S and W are there that begin at (0,0), end at (-12,-12)

How many lattice paths with step $S$ and $W$ are there that begin at $(0,0)$, end at $(-12,-12)$ and do not go through any of the points $(-1,-4), \space (-5,-3), \space (-9,-11)$? I'm unsure of how ...
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1answer
19 views

Need help understanding onto function

Let function $g$ from $V = \{1,2,3,4\}$ into V be defined by: $g(n)=3$. I'm having trouble understanding why $g$ is not onto. I understand why it is not one-to-one but, since all the $y$ in $Y$, are ...
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0answers
22 views

Min. color $N$ if every $4$ vertex subgraph has a $3$ degree vertex [duplicate]

If a graph has $N$ vertices and every $4$ vertex subgraph has a $3$ degree vertex then prove there is a vertex with degree $N-1$.
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22 views

Check if graphs are Eulerian

I've been checking whether these graphs are Eulerian; I've come to conclusion that all of them are Eulerian, because they're all connected and all the vertices are of even degree. However, when I ...
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20 views

How to combine possible permutations of two sets to find number of combined permutations

I hope the title accurately describes the question. I have a question that asks: There are 7 male swimmers and 5 female swimmers. If there is a gold, silver, and bronze medalist male swimmer, and a ...
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1answer
17 views

Determine whether each pair is $f(n) = O(g(n), f(n) = \Omega(g(n)), or f(n) = \Theta(g(n)).$

For the pair of functions, find whether it's $f(n) = O(g(n), f(n) = \Omega(g(n)), or f(n) = \Theta(g(n)):$ $a) f(n) = 12^n , g(n) = 7^n$ $b) f(n) = log_9(n^4), g(n) = log_9(n^5)$ I understand that: ...
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18 views

Practicing mathematical proofs in preparation for another course and could use some help [on hold]

I'm starting a course on Algorithms and the professor wants to test our induction and proof knowledge. Problem is, our prerequisite courses never focused on such material. I'm hoping someone could ...
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4answers
61 views

Show that if $m^2 + n^2 $ is divisible by $4$, then $mn$ is also divisible by $4$.

Show that if $m$ and $n$ are integers such that $m^2 + n^2 $ is divisible by $4$, then $mn$ is also divisible by $4$. I am not sure where to begin.
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2answers
40 views

prove that 2 does not go into $n^2 – 2$ without a remainder for odd $n$.

Prove that $2$ does not go into $n^2 – 2$ without a remainder for odd $n$. How do I approach this?
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9 views

Pinning 2015 polygons on a grid

Given 2 square grids with areas of 2015 units sq, each. Each of the grids is divided into 2015 polygons with an area of 1 unit sq. The grids are not necessarily identical in their division. We ...
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3answers
76 views

Cannot follow proof that $n! \leq en(n/e)^n$

prove that $n! \leq en(n/e)^n$ skip proof for base (n=1)... Assume it holds for $n-1$, verify for $n$. We have $n! = n* (n-1)! \leq n * e(n-1)(\frac{n-1}{e})^{n-1} $ by inductive assumption. we ...
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1answer
17 views

Network/graph theory -acyclic problem [on hold]

Consider an acyclic directed network of n vertices, labeled $i=1...n$, and suppose that the labels are assigned such that all edges run from vertices with higher labels to vertices with lower. Show ...
2
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1answer
30 views

Remove minimal number of elements

Given the numbers $ 1,2,..,2n + 1 $ , $ n > 0$ , remove as few numbers as possible so that among the remaining numbers no number is equal to the sum of two other numbers. After removal of first ...