Hot questions in Discrete Mathematics / GATE Overflow for GATE CSE

1 votes

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1801

NIELIT 2016 MAR Scientist C - Section B: 20
Degree of each vertex in $K_n$ is $n$ $n-1$ $n-2$ $2n-1$

Degree of each vertex in $K_n$ is $n$$n-1$$n-2$$2n-1$

admin

521 views

admin asked Apr 2, 2020

0 votes

1 answer

1802

Kenneth Rosen Edition 7 Exercise 1.7 Question 16 (Page No. 91)
Prove that if $m$ and $n$ are integers and $mn$ is even, then $m$ is even or $n$ is even.

Prove that if $m$ and $n$ are integers and $mn$ is even, then $m$ is even or $n$ is even.

Pooja Khatri

284 views

Pooja Khatri asked Apr 4, 2019

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0 answers

1803

Kenneth Rosen Edition 7 Exercise 8.1 Question 46 (Page No. 512)
Let $\{a_{n}\}$ be a sequence of real numbers. The backward differences of this sequence are defined recursively as shown next. The first difference $\triangledown a_{n}$ is $\triangledown a_{n} = a_{n} − a_{n−1}.$ The $(k + 1)^{\text{st}}$ ... $a_{n} = 4.$ $a_{n} = 2n.$ $a_{n} = n^{2}.$ $a_{n} = 2^{n}.$

Let $\{a_{n}\}$ be a sequence of real numbers. The backward differences of this sequence are defined recursively as shown next. The first difference $\triangledown a_{n}$...

admin

147 views

admin asked May 3, 2020

0 votes

0 answers

1804

Kenneth Rosen Edition 7 Exercise 6.2 Question 42 (Page No. 406)
Is the statement in question $41$ true if $24$ is replaced by $2?$ $23?$ $25?$ $30?$

Is the statement in question $41$ true if $24$ is replaced by$2?$$23?$$25?$$30?$

admin

283 views

admin asked Apr 29, 2020

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0 answers

1805

Kenneth Rosen Edition 7 Exercise 6.5 Question 50 (Page No. 434)
How many ways are there to distribute five distinguishable objects into three indistinguishable boxes?

How many ways are there to distribute five distinguishable objects into three indistinguishable boxes?

admin

206 views

admin asked May 1, 2020

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0 answers

1806

Kenneth Rosen Edition 7 Exercise 6.2 Question 34 (Page No. 406)
Assuming that no one has more than $1,000,000$ hairs on the head of any person and that the population of New York City was $8,008,278\:\text{in}\: 2010,$ show there had to be at least nine people in NewYork City in $2010$ with the same number of hairs on their heads.

Assuming that no one has more than $1,000,000$ hairs on the head of any person and that the population of New York City was $8,008,278\:\text{in}\: 2010,$ show there had ...

admin

287 views

admin asked Apr 29, 2020

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0 answers

1807

Kenneth Rosen Edition 7 Exercise 8.1 Question 24 (Page No. 511)
Find a recurrence relation for the number of bit sequences of length $n$ with an even number of $0s.$

Find a recurrence relation for the number of bit sequences of length $n$ with an even number of $0s.$

admin

189 views

admin asked May 2, 2020

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0 answers

1808

Kenneth Rosen Edition 7 Exercise 8.1 Question 23 (Page No. 511)
Find the recurrence relation satisfied by $S_{n},$ where $S_{n}$ is the number of regions into which three-dimensional space is divided by $n$ planes if every three of the planes meet in one point, but no four of the planes go through the same point. Find $S_{n}$ using iteration.

Find the recurrence relation satisfied by $S_{n},$ where $S_{n}$ is the number of regions into which three-dimensional space is divided by $n$ planes if every three of th...

admin

225 views

admin asked May 2, 2020

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0 answers

1809

Kenneth Rosen Edition 7 Exercise 6.5 Question 28 (Page No. 433)
Show that there are $C(n + r − q_{1} − q_{2} −\dots − q_{r} −1, n − q_{1} − q_{2} −\dots − q_{r})$ different unordered selections of $n$ objects of $r$ different types that include at least $q_{1}$ objects of type one, $q_{2}$ objects of type two $,\dots, $ and $q_{r}$ objects of type $r.$

Show that there are $C(n + r − q_{1} − q_{2} −\dots − q_{r} −1, n − q_{1} − q_{2} −\dots − q_{r})$ different unordered selections of $n$ objects of $r$ ...

admin

261 views

admin asked Apr 30, 2020

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0 answers

1810

Kenneth Rosen Edition 7 Exercise 6.1 Question 33 (Page No. 397)
How many strings of eight English letters are there that contain no vowels, if letters can be repeated? that contain no vowels, if letters cannot be repeated? that start with a vowel, if letters can be repeated? that start with a ... be repeated? that start and end with $X$ and contain at least one vowel, if letters can be repeated?

How many strings of eight English letters are therethat contain no vowels, if letters can be repeated?that contain no vowels, if letters cannot be repeated?that start wit...

admin

504 views

admin asked Apr 28, 2020

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0 answers

1811

Kenneth Rosen Edition 7 Exercise 8.1 Question 43 (Page No. 512)
Question $38-45$ involve the Reve's puzzle, the variation of the Tower of Hanoi puzzle with four pegs and $n$ disks. Before presenting these exercises, we describe the Frame-Stewart algorithm for moving the disks from peg $1$ to peg $4$ so that no disk is ... then $R(n) = \displaystyle{}\sum_{i = 1}^{k} i2^{i−1} − (t_{k} − n)2^{k−1}.$

Question $38–45$ involve the Reve’s puzzle, the variation of the Tower of Hanoi puzzle with four pegs and $n$ disks. Before presenting these exercises, we describe th...

admin

152 views

admin asked May 2, 2020

0 votes

1 answer

1812

Kenneth Rosen Edition 7 Exercise 6.1 Question 36 (Page No. 397)
How many functions are there from the set $\{1, 2,\dots,n\},$ where $n$ is a positive integer, to the set $\{0, 1\}?$

How many functions are there from the set $\{1, 2,\dots,n\},$ where $n$ is a positive integer, to the set $\{0, 1\}?$

admin

354 views

admin asked Apr 28, 2020

1 votes

1 answer

1813

JEST 2020
X AND Y is an arbitrary sets, F: $X\rightarrow Y$ show that a and b are equivalent F is one-one For all set Z and function g1: $Z\rightarrow X$ and g2: $Z\rightarrow X$, if $g1 \neq g2$ implies $f \bigcirc g1 \neq f \bigcirc g2$ Where $\bigcirc$ is a fucntion composition.

X AND Y is an arbitrary sets, F: $X\rightarrow Y$ show that a and b are equivalent F is one-oneFor all set Z and function g1: $Z\rightarrow X$ and g2: $Z\rightarrow X$, ...

vivek_mishra

863 views

vivek_mishra asked Feb 17, 2020

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0 answers

1814

Kenneth Rosen Edition 7 Exercise 6.6 Question 10 (Page No. 438)
Show that Algorithm $1$ produces the next larger permutation in lexicographic order.

Show that Algorithm $1$ produces the next larger permutation in lexicographic order.

admin

164 views

admin asked May 1, 2020

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0 answers

1815

Kenneth Rosen Edition 7 Exercise 6.5 Question 54 (Page No. 434)
How many ways are there to distribute five indistinguishable objects into three indistinguishable boxes?

How many ways are there to distribute five indistinguishable objects into three indistinguishable boxes?

admin

213 views

admin asked May 1, 2020

1 votes

2 answers

1816

CMI2016-A-5
A dodecahedron is a regular solid with $12$ faces, each face being a regular pentagon. How many edges are there? And how many vertices? $60$ edges and $20$ vertices $30$ edges and $20$ vertices $60$ edges and $50$ vertices $30$ edges and $50$ vertices

A dodecahedron is a regular solid with $12$ faces, each face being a regular pentagon. How many edges are there? And how many vertices?$60$ edges and $20$ vertices$30$ ed...

go_editor

579 views

go_editor asked Dec 30, 2016

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0 answers

1817

Kenneth Rosen Edition 7 Exercise 6.4 Question 32 (Page No. 422)
Prove the binomial theorem using mathematical induction.

Prove the binomial theorem using mathematical induction.

admin

173 views

admin asked Apr 30, 2020

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0 answers

1818

Kenneth Rosen Edition 7 Exercise 8.1 Question 37 (Page No. 512)
Question $33-37$ deal with a variation of the $\textbf{Josephus problem}$ described by Graham, Knuth, and Patashnik in $[G_{r}K_{n}P_{a}94].$ This problem is based on an account by the historian Flavius Josephus, who was part of a band of $41$ ... $J (100), J (1000),\: \text{and}\: J (10,000)$ from your formula for $J (n).$

Question $33–37$ deal with a variation of the $\textbf{Josephus problem}$ described by Graham, Knuth, and Patashnik in $[G_{r}K_{n}P_{a}94].$ This problem is based on a...

admin

172 views

admin asked May 2, 2020

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0 answers

1819

Kenneth Rosen Edition 7 Exercise 8.1 Question 1 (Page No. 510)
Use mathematical induction to verify the formula derived in Example $2$ for the number of moves required to complete the Tower of Hanoi puzzle.

Use mathematical induction to verify the formula derived in Example $2$ for the number of moves required to complete the Tower of Hanoi puzzle.

admin

195 views

admin asked May 1, 2020

0 votes

0 answers

1820

Kenneth Rosen Edition 7 Exercise 6.1 Question 56 (Page No. 398)
The name of a variable in the C programming language is a string that can contain uppercase letters, lowercase letters, digits, or underscores. Further, the first character in the string must be a letter, either uppercase or lowercase ... can be named in C? (Note that the name of a variable may contain fewer than eight characters.)

The name of a variable in the C programming language is a string that can contain uppercase letters, lowercase letters, digits, or underscores. Further, the first charact...

admin

320 views

admin asked Apr 28, 2020

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