Recent questions tagged kenneth-rosen / GATE Overflow for GATE CSE

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751

Kenneth Rosen Edition 7 Exercise 1.6 Question 17 (Page No. 79)
What is wrong with this argument? Let $H(x)$ be “$x$ is happy.” Given the premise $\exists x H(x)$, we conclude that $H(Lola)$. Therefore, Lola is happy.

What is wrong with this argument? Let $H(x)$ be “$x$ is happy.” Given the premise $\exists x H(x)$, we conclude that $H(Lola)$. Therefore, Lola is happy.

Pooja Khatri

364 views

Pooja Khatri asked Mar 19, 2019

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752

Kenneth Rosen Edition 7 Exercise 1.6 Question 16 (Page No. 79)
For each of these arguments determine whether the argument is correct or incorrect and explain why. Everyone enrolled in the university has lived in a dormitory. Mia has never lived in a dormitory. Therefore,Mia is not enrolled ... set at least a dozen traps. Hamilton is a lobsterman. Therefore, Hamilton sets at least a dozen traps

For each of these arguments determine whether the argument is correct or incorrect and explain why.Everyone enrolled in the university has lived in a dormitory. Mia has n...

Pooja Khatri

529 views

Pooja Khatri asked Mar 19, 2019

2 votes

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753

Kenneth Rosen Edition 7 Exercise 1.6 Question 15 (Page No. 79)
For each of these arguments determine whether the argument is correct or incorrect and explain why. All students in this class understand logic. Xavier is a student in this class. Therefore, Xavier understands logic. Every computer ... granola every day is healthy. Linda is not healthy. Therefore, Linda does not eat granola every day.

For each of these arguments determine whether the argument is correct or incorrect and explain why.All students in this class understand logic. Xavier is a student in thi...

Pooja Khatri

1.1k views

Pooja Khatri asked Mar 19, 2019

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754

Kenneth Rosen Edition 7 Exercise 1.6 Question 14 (Page No. 79)
For each of these arguments, explain which rules of inference are used for each step. Linda, a student in this class, owns a red convertible.Everyone who owns a red convertible has gotten at least one speeding ticket. ... to France. Everyone who goes to France visits the Louvre. Therefore, someone in this class has visited the Louvre.

For each of these arguments, explain which rules of inference are used for each step.“Linda, a student in this class, owns a red convertible.Everyone who owns a red con...

Pooja Khatri

898 views

Pooja Khatri asked Mar 19, 2019

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755

Kenneth Rosen Edition 7 Exercise 1.6 Question 13 (Page No. 79)
For each of these arguments, explain which rules of inference are used for each step. Doug, a student in this class, knows how to write programs in JAVA. Everyone who knows how to write programs in JAVA can get a high- ... has never seen the ocean. Therefore, someone who lives within 50 miles of the ocean has never seen the ocean.

For each of these arguments, explain which rules of inference are used for each step.“Doug, a student in this class, knows how to write programs in JAVA. Everyone who k...

Pooja Khatri

1.5k views

Pooja Khatri asked Mar 19, 2019

1 votes

1 answer

756

Kenneth Rosen Edition 7 Exercise 1.6 Question 9 (Page No. 78)
For each of these collections of premises, what relevant conclusion or conclusions can be drawn? Explain the rules of inference used to obtain each conclusion from the premises. If I take the day off, it either rains or snows. I took ... gnaw their food. Mice are rodents. Rabbits do not gnaw their food. Bats are not ro-dents.

For each of these collections of premises, what relevant conclusion or conclusions can be drawn? Explain the rules of inference used to obtain each conclusion from the pr...

Pooja Khatri

3.7k views

Pooja Khatri asked Mar 19, 2019

0 votes

1 answer

757

Kenneth Rosen Edition 7 Exercise 1.6 Question 8 (Page No. 78)
What rules of inference are used in this argument? “No man is an island. Manhattan is an island. Therefore, Manhattan is not a man.”

What rules of inference are used in this argument? “No man is an island. Manhattan is an island. Therefore, Manhattan is not a man.”

Pooja Khatri

2.6k views

Pooja Khatri asked Mar 19, 2019

0 votes

0 answers

758

Kenneth Rosen Edition 7 Exercise 1.6 Question 7 (Page No. 78)
What rules of inference are used in this famous argument? “All men are mortal. Socrates is a man. Therefore,Socrates is mortal.”

What rules of inference are used in this famous argument? “All men are mortal. Socrates is a man. Therefore,Socrates is mortal.”

Pooja Khatri

741 views

Pooja Khatri asked Mar 19, 2019

0 votes

0 answers

759

Kenneth Rosen Edition 7 Exercise 1.6 Question 5 (Page No. 78)
Use rules of inference to show that the hypotheses “Randy works hard,” “If Randy works hard, then he is a dull boy,”and “If Randy is a dull boy, then he will not get the job”imply the conclusion “Randy will not get the job.”

Use rules of inference to show that the hypotheses “Randy works hard,” “If Randy works hard, then he is a dull boy,”and “If Randy is a dull boy, then he will no...

Pooja Khatri

695 views

Pooja Khatri asked Mar 19, 2019

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760

Kenneth Rosen Edition 7 Exercise 1.6 Question 4 (Page No. 78)
What rule of inference is used in each of these arguments? Kangaroos live in Australia and are marsupials. There-fore, kangaroos are marsupials. It is either hotter than 100 degrees today or the pollution is dangerous. It ... understand the material . Therefore ,If I work all night on this homework, Then I will understand the material.

What rule of inference is used in each of these arguments?Kangaroos live in Australia and are marsupials. There-fore, kangaroos are marsupials.It is either hotter than 10...

Pooja Khatri

615 views

Pooja Khatri asked Mar 19, 2019

0 votes

0 answers

761

Kenneth Rosen Edition 7 Exercise 1.6 Question 3 (Page No. 78)
What rule of inference is used in each of these arguments? Alice is a mathematics major. Therefore, Alice is either a mathematics major or a computer science major. Jerry is a mathematics major and a computer science major. Therefore, ... stay in the sun too long, then I will sunburn. Therefore, if I go swimming, then I will sunburn

What rule of inference is used in each of these arguments?Alice is a mathematics major. Therefore, Alice is either a mathematics major or a computer science major.Jerry i...

Pooja Khatri

386 views

Pooja Khatri asked Mar 19, 2019

0 votes

0 answers

762

Kenneth Rosen Edition 7 Exercise 1.5 Question 49 (Page No. 68)
Show that $\forall x P(x) \wedge \exists x Q(x)$ is logically equivalent to $\forall x \exists y (P(x) \wedge Q(y))$ ... from propositional variables,predicates,T, and F using logical connectives and quantifiers is equivalent to a statement in prenex normal form.

Show that $\forall x P(x) \wedge \exists x Q(x)$ is logically equivalent to $\forall x \exists y (P(x) \wedge Q(y))$, where all quantifiers have the same nonempty domain....

Pooja Khatri

287 views

Pooja Khatri asked Mar 19, 2019

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763

Kenneth Rosen Edition 7 Exercise 1.5 Question 48 (Page No. 68)
Show that $\forall x P(x) \vee \forall x Q(x)$ and $\forall x \forall y (P(x) \vee Q(y))$, where all quantifiers have the same nonempty domain, are logically equivalent . (The new variable $y$ is used to combine the quantifications correctly.)

Show that $\forall x P(x) \vee \forall x Q(x)$ and $\forall x \forall y (P(x) \vee Q(y))$, where all quantifiers have the same nonempty domain, are logically equivalent ...

Pooja Khatri

229 views

Pooja Khatri asked Mar 19, 2019

0 votes

0 answers

764

Kenneth Rosen Edition 7 Exercise 1.5 Question 47 (Page No. 68)
Show that the two statements $\sim \exists x \forall y P(x,y)$ and $\forall x \exists y \sim P(x,y)$ , where both quantifiers over the first variable in $P(x,y)$ have the same domain , and both quantifiers over the second variable in $P(x,y)$ have the same domain, are logically equivalent.

Show that the two statements $\sim \exists x \forall y P(x,y)$ and $\forall x \exists y \sim P(x,y)$ , where both quantifiers over the first variable in $P(x,y)$ have th...

Pooja Khatri

199 views

Pooja Khatri asked Mar 19, 2019

0 votes

0 answers

765

Kenneth Rosen Edition 7 Exercise 1.5 Question 46 (Page No. 68)
Determine the truth value of the statement $\exists x \forall y (x<=y^2)$ if the domain for the variables consists of he positive real numbers. the integers. the nonzero real numbers.

Determine the truth value of the statement $\exists x \forall y (x<=y^2)$ if the domain for the variables consists ofhe positive real numbers.the integers.the nonzero rea...

Pooja Khatri

217 views

Pooja Khatri asked Mar 19, 2019

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766

Kenneth Rosen Edition 7 Exercise 1.5 Question 45 (Page No. 68)
Determine the truth value of the statement $\forall x \exists y (xy=1)$ if the domain for the variables consists of the nonzero real numbers. the nonzero integers. the positive real numbers.

Determine the truth value of the statement $\forall x \exists y (xy=1)$ if the domain for the variables consists ofthe nonzero real numbers.the nonzero integers.the posit...

Pooja Khatri

266 views

Pooja Khatri asked Mar 19, 2019

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767

Kenneth Rosen Edition 7 Exercise 1.5 Question 40 (Page No. 68)
Find a counterexample, if possible ,to these universally quantified statements, where the domain for all variables consists of all integers. $\forall x \exists y (x=1/y)$ $\forall x \exists y (y^2 -x <100)$ $\forall x \forall y (x^2 \neq y^3)$

Find a counterexample, if possible ,to these universally quantified statements, where the domain for all variables consists of all integers.$\forall x \exists y (x=1/y)$$...

Pooja Khatri

248 views

Pooja Khatri asked Mar 19, 2019

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768

Kenneth Rosen Edition 7 Exercise 1.5 Question 39 (Page No. 68)
Find a counterexample, if possible, to these universally quantified statements, where the domain for all variables consists of all integers. $\forall x \forall y (x^2 = y^2 \rightarrow x =y)$ $\forall x \exists y (y^2=x)$ $\forall x \forall y (xy>=x)$

Find a counterexample, if possible, to these universally quantified statements, where the domain for all variables consists of all integers.$\forall x \forall y (x^2 = y^...

Pooja Khatri

388 views

Pooja Khatri asked Mar 19, 2019

0 votes

0 answers

769

Kenneth Rosen Edition 7 Exercise 1.5 Question 37 (Page No. 68)
Express each of these statements using quantifiers. Then form the negation of the statement so that no negation is to the left of a quantifier. Next, express the negation in simple English. (Do not simply use the phrase It is not ... a movie with Kevin Bacon or has been in a movie with someone who has been in a movie with Kevin Bacon

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

Pooja Khatri

419 views

Pooja Khatri asked Mar 19, 2019

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0 answers

770

Kenneth Rosen Edition 7 Exercise 1.5 Question 36 (Page No. 68)
Express each of these statements using quantifiers. Then form the negation of the statement so that no negation is to the left of a quantifier. Next, express the negation in simple English. (Do not simply use the phrase It ... solved every exercise in this book. No student has solved at least one exercise in every section of this book.

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

Pooja Khatri

804 views

Pooja Khatri asked Mar 19, 2019

0 votes

0 answers

771

Kenneth Rosen Edition 7 Exercise 1.5 Question 34 (Page No. 66)
Find a common domain for the variables $x,y$, and $z$ for which the statement $\forall x \forall y ((x \neq y) \rightarrow \forall z (z=x) \vee (z=y))$ is true and another domain for which it is false.

Find a common domain for the variables $x,y$, and $z$ for which the statement $\forall x \forall y ((x \neq y) \rightarrow \forall z (z=x) \vee (z=y))$ is true and anothe...

Pooja Khatri

299 views

Pooja Khatri asked Mar 19, 2019

1 votes

0 answers

772

Kenneth Rosen Edition 7 Exercise 1.5 Question 33 (Page No. 66)
Rewrite each of these statements so that negations ap-pear only within predicates (that is, so that no negation is outside a quantifier or an expression involving logical connectives). $\sim \forall x \forall y P(x,y)$ ... $\sim \forall x (\exists y \forall z P(x,y,z) \wedge \exists z \forall y P(x,y,z))$

Rewrite each of these statements so that negations ap-pear only within predicates (that is, so that no negation is outside a quantifier or an expression involving logical...

Pooja Khatri

460 views

Pooja Khatri asked Mar 19, 2019

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773

Kenneth Rosen Edition 7 Exercise 1.5 Question 32 (Page No. 66)
Express the negations of each of these statements so that all negation symbols immediately precede predicates. $\exists z \forall y \forall x T(x,y,z)$ $\exists x \exists y P(x,y) \wedge \forall x \forall y Q(x,y)$ $\exists x \exists y(Q(x,y) \leftrightarrow Q(y,x))$ $\forall y \exists x \exists z (T(x,y,z) \vee Q(x,y))$

Express the negations of each of these statements so that all negation symbols immediately precede predicates.$\exists z \forall y \forall x T(x,y,z)$$\exists x \exists y...

Pooja Khatri

340 views

Pooja Khatri asked Mar 19, 2019

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774

Kenneth Rosen Edition 7 Exercise 1.5 Question 31 (Page No. 66)
Express the negations of each of these statements so that all negation symbols immediately precede predicates. $\forall x \exists y \forall z T(x,y,z)$ $\forall x \exists y P(x,y) \vee \forall x \exists y Q(x,y)$ $\forall x \exists y (P(x,y) \wedge \exists z R(x,y,z))$ $\forall x \exists y( P(x,y) \rightarrow Q(x,y))$

Express the negations of each of these statements so that all negation symbols immediately precede predicates.$\forall x \exists y \forall z T(x,y,z)$$\forall x \exists y...

Pooja Khatri

323 views

Pooja Khatri asked Mar 19, 2019

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775

Kenneth Rosen Edition 7 Exercise 1.5 Question 30 (Page No. 66)
Rewrite each of these statements so that negations appear only within predicates (that is, so that no negation is outside a quantifier or an expression involving logical connectives). $\sim \exists y \exists x P(x,y)$ $\sim \forall x \exists y P(x,y)$ ... $\sim \exists y (\forall x \exists z T(x,y,z) \vee \exists x \forall z U(x,y,z))$

Rewrite each of these statements so that negations appear only within predicates (that is, so that no negation is outside a quantifier or an expression involving logical ...

Pooja Khatri

496 views

Pooja Khatri asked Mar 19, 2019

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776

Kenneth Rosen Edition 7 Exercise 1.5 Question 29 (Page No. 66)
Suppose the domain of the propositions 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. $\forall x \forall y P(x,y)$ $\exists x \exists y P(x,y)$ $\exists x \forall y P(x,y)$ $\forall y \exists x P(x,y)$

Suppose the domain of the propositions 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 us...

Pooja Khatri

241 views

Pooja Khatri asked Mar 19, 2019

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777

Kenneth Rosen Edition 7 Exercise 1.5 Question 28 (Page No. 66)
Determine the truth value of each of these statements if the domain of each variable consists of all real numbers. $\forall x \exists y (x^2 = y)$ $\forall x \exists y ( x= y^2)$ $\exists x \forall y (xy =0)$ ... $\forall x \exists y (x+y =2 \wedge 2x-y =1)$ $\forall x \forall y \exists z(z= (x+y)/2)$

Determine the truth value of each of these statements if the domain of each variable consists of all real numbers.$\forall x \exists y (x^2 = y)$$\forall x \exists y ( x=...

Pooja Khatri

399 views

Pooja Khatri asked Mar 19, 2019

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0 answers

778

Kenneth Rosen Edition 7 Exercise 1.5 Question 27 (Page No. 66)
Determine the truth value of each of these statements if the domain for all variables consists of all integers. $\forall n \exists m (n^2 <m)$ $\exists n \forall m (n <m^2)$ $\forall n \exists m(n+m=0)$ $\exists n \forall m (nm=m)$ ... $\exists n \exists m (n+m = 4 \wedge n-m =2)$ $\forall n \forall m \exists p(p= (m+n)/2)$

Determine the truth value of each of these statements if the domain for all variables consists of all integers.$\forall n \exists m (n^2 <m)$$\exists n \forall m (n <m^2)...

Pooja Khatri

6.0k views

Pooja Khatri asked Mar 19, 2019

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1 answer

779

Kenneth Rosen Edition 7 Exercise 1.5 Question 26 (Page No. 66)
Let $Q(x, y)$ be the statement “ $x+y=x−y.$ ” If the domain for both variables consists of all integers, what are the truth values? $Q (1,1)$ $Q(2,0)$ $\forall y Q(1,y)$ $\exists x Q(x,2)$ $\exists x \exists y Q(x,y)$ $\forall x \exists y Q(x,y)$ $\exists x \forall y Q(x,y)$ $\forall y \exists x Q(x,y)$ $\forall x \forall y Q(x,y)$

Let $Q(x, y)$ be the statement “ $x+y=x−y.$ ” If the domain for both variables consists of all integers, what are the truth values?$Q (1,1)$$Q(2,0)$$\forall y Q(1,y...

Pooja Khatri

601 views

Pooja Khatri asked Mar 19, 2019

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0 answers

780

Kenneth Rosen Edition 7 Exercise 1.5 Question 25 (Page No. 66)
Translate each of these nested quantifications into an English statement that expresses a mathematical fact. The domain in each case consists of all real numbers. $\exists x \forall y (xy=y)$ ... $\forall x \forall y \exists z (x+y =z)$

Translate each of these nested quantifications into an English statement that expresses a mathematical fact. The domain in each case consists of all real numbers.$\exists...

Pooja Khatri

496 views

Pooja Khatri asked Mar 19, 2019

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title	title:apple
content	content:apple
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force match	+apple
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