Let W(x. y) mean that student .x has visited website y,

Chapter 7, Problem 5E

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QUESTION:

Let \(W(x, y)\) mean that student \(x\) has visited website \(y\), where the domain for \(x\) consists of all students in your school and the domain for y consists of all websites. Express each of these statements by a simple English sentence.

a) \(W\)(Sarah Smith, www.att.com)

b) \(\exists x W(x\) www. imdb.org)

c) \(\existsyW\)(José Orez, y)

d) \(\existsy(W(\)Ashok Puri, \(y)\wedge W(\) Cindy Yoon, y))

e) \(\exists y \forall z(y \neq(\) David Belcher \() \wedge(W(\)David Belcher, \(z) \rightarrow W(y, z)))\)

f) \(\exists x \exists y \forall z((x \neq y) \wedge(W(x, z) \leftrightarrow W(y, z)))\)

Equation Transcription:

∃xW(x

∃yW

∃y∀z(y

∃x∃y∀z((x  y) ∧ (W (x, z) ↔ W (y, z)))

Text Transcription:

W (x, y)

\exists x W(x

\existsyW

\exists y \forall z(y \neq

exists x \exists y \forall z((x \neq y) \wedge(W(x, z) \leftrightarrow W(y, z)))

Questions & Answers

QUESTION:

Let \(W(x, y)\) mean that student \(x\) has visited website \(y\), where the domain for \(x\) consists of all students in your school and the domain for y consists of all websites. Express each of these statements by a simple English sentence.

a) \(W\)(Sarah Smith, www.att.com)

b) \(\exists x W(x\) www. imdb.org)

c) \(\existsyW\)(José Orez, y)

d) \(\existsy(W(\)Ashok Puri, \(y)\wedge W(\) Cindy Yoon, y))

e) \(\exists y \forall z(y \neq(\) David Belcher \() \wedge(W(\)David Belcher, \(z) \rightarrow W(y, z)))\)

f) \(\exists x \exists y \forall z((x \neq y) \wedge(W(x, z) \leftrightarrow W(y, z)))\)

Equation Transcription:

∃xW(x

∃yW

∃y∀z(y

∃x∃y∀z((x  y) ∧ (W (x, z) ↔ W (y, z)))

Text Transcription:

W (x, y)

\exists x W(x

\existsyW

\exists y \forall z(y \neq

exists x \exists y \forall z((x \neq y) \wedge(W(x, z) \leftrightarrow W(y, z)))

ANSWER:

Solution:

Step1

Given that

Suppose W(x. y) mean that student .x has visited website y, where the domain for .x consists of all students in our school and the domain for y consists of all websites.

Step2

To find

Express each of these statements by a simple English sentence.

Step3

From the given statement we are finding that

a.  

 means Sarah Smith has gone by www.att.com.

Step4

b.

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