Recent questions in Discrete Mathematics / GATE Overflow for GATE CSE

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2011

Kenneth Rosen Edition 7 Exercise 1.4 Question 41 (Page No. 55)
Express each of these system specifications using predicates, quantifiers, and logical connectives. At least one mail message, among the nonempty set of messages, can be saved if there is a disk with more than 10 kilobytes of free ... participant on the conference call whom the host of the call did not put on a special list was billed.

Express each of these system specifications using predicates, quantifiers, and logical connectives.At least one mail message, among the nonempty set of messages, can be s...

Pooja Khatri

1.2k views

Pooja Khatri asked Mar 18, 2019

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2012

Kenneth Rosen Edition 7 Exercise 1.4 Question 40 (Page No. 55)
Express each of these system specifications using predicates, quantifiers, and logical connectives. When there is less than 30 megabytes free on the hard disk, a warning message is sent to all users. No directories in the file ... are at least 8 megabytes of memory available and the connection speed is at least 56 kilobits per second.

Express each of these system specifications using predicates, quantifiers, and logical connectives.When there is less than 30 megabytes free on the hard disk, a warning m...

Pooja Khatri

843 views

Pooja Khatri asked Mar 18, 2019

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2013

Kenneth Rosen Edition 7 Exercise 1.4 Question 39 (Page No. 55)
Translate these specifications into English where $F(p)$ is Printer $p$ is out of service, $B(p)$ is Printer $p$ is busy, $L(j )$ is Print job $j$ is lost, and $Q(j )$is Print job $j$ ... $(\forall p B(p) \wedge \forall j Q(j)) \rightarrow \exists j L(j)$

Translate these specifications into English where $F(p)$ is“Printer $p$ is out of service,”$B(p)$ is “Printer $p$ is busy,”$L(j )$ is “Print job $j$ is lost,”...

Pooja Khatri

513 views

Pooja Khatri asked Mar 18, 2019

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2014

Kenneth Rosen Edition 7 Exercise 1.4 Question 38 (Page No. 55)
Translate these system specifications into English where the predicate $S(x,y)$ is $x$ is in state $y$ and where the domain for $x$ and $y$ consists of all system and all possible states, respectively. $\exists x S(x, open)$ ... $\exists x \sim S(x, available )$ $\forall x \sim S(x, working)$

Translate these system specifications into English where the predicate $S(x,y)$ is “$x$ is in state $y$ “ and where the domain for $x$ and $y$ consists of all system ...

Pooja Khatri

321 views

Pooja Khatri asked Mar 18, 2019

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2015

Kenneth Rosen Edition 7 Exercise 1.4 Question 37 (Page No. 55)
Express each of these statements using predicates and quantifiers. A passenger on an airline qualifies as an elite flyer if the passenger flies more than 25,000 miles in a year or takes more than 25 flights during that year. A man ... degree. There is a student who has taken more than 21 credit hours in a semester and received all A's.

Express each of these statements using predicates and quantifiers.A passenger on an airline qualifies as an elite flyer if the passenger flies more than 25,000 miles in a...

Pooja Khatri

668 views

Pooja Khatri asked Mar 18, 2019

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2016

Kenneth Rosen Edition 7 Exercise 1.4 Question 36 (Page No. 55)
Find a counterexample, if possible, to these universally quantified statements, where the domain for all variables consists of all real numbers. $\forall x (x^2 \neq x)$ $\forall x (x^2 \neq 2)$ $\forall x (|x| >0)$

Find a counterexample, if possible, to these universally quantified statements, where the domain for all variables consists of all real numbers.$\forall x (x^2 \neq x)$$\...

Pooja Khatri

314 views

Pooja Khatri asked Mar 18, 2019

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2017

Kenneth Rosen Edition 7 Exercise 1.4 Question 35 (Page No. 55)
Find a counterexample, if possible, to these universallyquantified statements, where the domain for all variablesconsists of all integers. $\forall x(x^2 >= x)$ $\forall x (x>0 \vee x<0)$ $\forall x (x=1)$

Find a counterexample, if possible, to these universallyquantified statements, where the domain for all variablesconsists of all integers.$\forall x(x^2 >= x)$$\forall x ...

Pooja Khatri

194 views

Pooja Khatri asked Mar 18, 2019

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2018

Kenneth Rosen Edition 7 Exercise 1.4 Question 33 (Page No. 55)
Express the negation of these propositions using quantifiers, and then express the negation in English. Some drivers do not obey the speed limit. All Swedish movies are serious. No one can keep a secret. There is someone in this class who does not have a good attitude.

Express the negation of these propositions using quantifiers, and then express the negation in English.Some drivers do not obey the speed limit.All Swedish movies are ser...

Pooja Khatri

629 views

Pooja Khatri asked Mar 18, 2019

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2019

Kenneth Rosen Edition 7 Exercise 1.4 Question 33 (Page No. 55)
Express each of these statements using quantifiers. Then form the negation of the statement so that no negation is to the left of quantifier. Next, express the negation in simple English. (Do not simply use the phrase It is not the ... can fly. There is no dog that can talk. There is no one in this class who knows French and Russian.

Express each of these statements using quantifiers. Then form the negation of the statement so that no negation is to the left of quantifier. Next, express the negation i...

Pooja Khatri

470 views

Pooja Khatri asked Mar 18, 2019

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2020

Kenneth Rosen Edition 7 Exercise 1.4 Question 32 (Page No. 55)
Express each of these statements using quantifiers. Then form the negation of the statement so that no negation is to the left of quantifier. Next, express the negation in simple English. (Do not simply use the phrase It is not ... add. Every koala can climb. No monkey can speak French. There exists a pig that can swim and catch fish.

Express each of these statements using quantifiers. Then form the negation of the statement so that no negation is to the left of quantifier. Next, express the negation i...

Pooja Khatri

530 views

Pooja Khatri asked Mar 18, 2019

1 votes

1 answer

2021

Kenneth Rosen Edition 7 Exercise 1.4 Question 31 (Page No. 54)
Suppose that the domain of $Q(x,y,z)$ consists of triples $x,y,z,$ where $x=0,1$ or $2$ , $y=0$ or $1,$ and $z=0$ or $1.$ Write out these propositions using disjunctions and conjunctions. $a)$ $\forall y \;\;\;Q(0, y, 0)$ $b)$ $\exists x\; \;\; Q(x, 1, 1)$ $c)$ $\exists z \;¬Q(0, 0, z)$ $d)$ $\exists x\;¬Q(x, 0, 1)$

Suppose that the domain of $Q(x,y,z)$ consists of triples $x,y,z,$ where $x=0,1$ or $2$ , $y=0$ or $1,$ and $z=0$ or $1.$ Write out these propositions using disjunctions ...

Pooja Khatri

557 views

Pooja Khatri asked Mar 18, 2019

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2022

Kenneth Rosen Edition 7 Exercise 1.4 Question 30 (Page No. 54)
Suppose the domain of the propositional function $P(x,y)$ consists of pairs $x$ and $y$ , where $x$ is 1,2 or 3 and $y$ is 1,2 or 3 . Write out these propositions using disjunctions and conjunctions. $\exists x P(x,3)$ $\forall y P(1,y)$ $\exists y \sim p(2,y)$ $\forall x \sim P(x,2)$

Suppose the domain of the propositional function $P(x,y)$ consists of pairs $x$ and $y$ , where $x$ is 1,2 or 3 and $y$ is 1,2 or 3 . Write out these propositions using d...

Pooja Khatri

443 views

Pooja Khatri asked Mar 18, 2019

3 votes

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2023

Kenneth Rosen Edition 7 Exercise 2.2 Question 49 (Page No. 137)
Find ${\displaystyle \bigcup _{i=1}^{\infty }A_{i}} and \bigcup_{i=1}^{\infty} A_{i}$ if for every positive integer i, a) Ai = {i, i + 1, i + 2, . . .}. b) Ai = {0, i}. c) Ai = (0, i), that is, the set of real numbers x with 0 < x < i. d) Ai = (i,∞), that is, the set of real numbers x with x > i.

Find ${\displaystyle \bigcup _{i=1}^{\infty }A_{i}} and \bigcup_{i=1}^{\infty} A_{i}$ if for every positive integer i,a) Ai = {i, i + 1, i + 2, . . .}.b) Ai = {0, i}.c) A...

sumitr

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sumitr asked Mar 17, 2019

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2024

Graph Decomposition
What is Graph Decomposition & is it in the syllabus? If it is then please can anyone share some online resources for it. Thank you.

What is Graph Decomposition & is it in the syllabus?If it is then please can anyone share some online resources for it. Thank you.

noxevolution

251 views

noxevolution asked Mar 17, 2019

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2025

Kenneth Rosen Edition 7 Exercise 1.4 Question 28 (Page No. 54)
Translate each of these statements into logical expression using predicates, quantifiers, and logical connectives. Something is not in the correct place. All tools are in the correct place and are in excellent condition. Everyone is in ... in excellent condition. One of your tools is not in the correct, but it is in excellent condition.

Translate each of these statements into logical expression using predicates, quantifiers, and logical connectives.Something is not in the correct place.All tools are in t...

Pooja Khatri

686 views

Pooja Khatri asked Mar 16, 2019

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2026

Kenneth Rosen Edition 7 Exercise 1.4 Question 27 (Page No. 54)
Translate each of these statements into logical expression in three different ways by varying the domain and by using predicates with one and with two variables. A student in your school has lived in Vietnam. There is a student in ... Prolog, and C++. Everyone in your class enjoys Thai food. Someone in your class does not play hockey.

Translate each of these statements into logical expression in three different ways by varying the domain and by using predicates with one and with two variables.A student...

Pooja Khatri

1.3k views

Pooja Khatri asked Mar 16, 2019

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2027

Kenneth Rosen Edition 7 Exercise 1.4 Question 26 (Page No. 54)
Translate each of these statements into logical expression in three different ways by varying the domain and by using predicates with one and with two variables. Someone in your school has visited Uzbekistan. Everyone in your class ... person in your school who is not happy. Everyone in your school was born in the twentieth century.

Translate each of these statements into logical expression in three different ways by varying the domain and by using predicates with one and with two variables.Someone i...

Pooja Khatri

664 views

Pooja Khatri asked Mar 16, 2019

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2028

Kenneth Rosen Edition 7 Exercise 1.4 Question 22 (Page No. 54)
For each of these statements find a domain for which the statement is true and a domain for which the statement is false. Everyone speak Hindi. There is someone older than 21 years. Everyone two people have the same first name. Someone knows more than two other people.

For each of these statements find a domain for which the statement is true and a domain for which the statement is false.Everyone speak Hindi.There is someone older than ...

Pooja Khatri

772 views

Pooja Khatri asked Mar 16, 2019

0 votes

1 answer

2029

Kenneth Rosen Edition 7 Exercise 1.4 Question 21 (Page No. 54)
For each fo these statements find a domain for which the statements is true and a domain for which the statement is false. Everyone is studying discrete mathematics. Everyone is older than 21 years. Everyone two people have the same mother. No two different people have the same grandmother.

For each fo these statements find a domain for which the statements is true and a domain for which the statement is false.Everyone is studying discrete mathematics.Everyo...

Pooja Khatri

6.2k views

Pooja Khatri asked Mar 16, 2019

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2030

Kenneth Rosen Edition 7 Exercise 1.4 Question 20 (Page No. 54)
Suppose that the domain of the propositional function $P(x)$ consists of $-5,-3,-1,1,3,5.$ Express these statements without using quantifiers, instead using only negations, disjunctions, and conjunctions. $\exists x p(x)$ $\forall x p(x)$ ... $\exists x (\sim p(x)) \wedge \forall x ((x<0) \rightarrow p(x))$

Suppose that the domain of the propositional function $P(x)$ consists of $-5,-3,-1,1,3,5.$ Express these statements without using quantifiers, instead using only negation...

Pooja Khatri

450 views

Pooja Khatri asked Mar 16, 2019

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