/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q28P Let R鈯單澛� kbe a -kary relatio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q28P (page 271)

Let R鈯�螡 kbe a -kary relation. Say that Ris definable in Th(螡,+)if we can give a formula蠁with kfree variablesx1,...,xksuch that for all,a1,...,ak鈭�螡,蠁(a1,...,ak)is true exactly when .a1,...,ak鈭�RShow that each of the following relations is definable in.Th(螡,+)

a.R0={0}

b.R1={1}

c.R=={(a,a)|a鈭�螡}

d.R<={(a,b)|a,b鈭�螡anda<b}

Short Answer

Expert verified

a).鈭�0(x)=鈭赌y[x+y=y]

b). .data-custom-editor="chemistry" 鈭�1(x)=鈭赌y[x+y=y+1]

c).鈭�=(x,y)=鈭赌z[鈭�0(z)鈫�x+z=y]

d).鈭�<(x,y)=鈭赌z[鈭�0(z)鈫�x+z<y]

Step by step solution

01

Solution (a)

In the case R0={0}

There is only one value 0鈥樷赌�.

If we add0 in variabley鈭�螡, there will be no effect on y

So the formula: 鈭赌x鈭�R0鈭赌y[x+y鈫�0+y]

This will become as: 鈭�0(x)=鈭赌y[x+y=y]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Let be two disjoint languages. Say that language separates if A鈯�CandB鈯�C'. Describe two disjoint Turing-recognizable languages that aren鈥檛 separable by any decidable language.

Prove that there exist two languages that are Turing-incomparable鈥攖hat is,A 'TB where B'T A.

Give a model of the sentence

蠁It=鈭�鈭赌X,Y[R1(x,x)]鈭�鈭赌x.y[R1(x,y)鈫�(R1(y,x)]鈭�鈭赌x,y,z[(R1(x,y)鈭�R1(y,z))鈫�R1(x,z)]

Show that the set of incompressible strings is undecidable.

LetATM*={M,wM is an oracle TM and MTMAaccepts w}. Show that ATM'is undecidable relative to ATM.
See all solutions

Recommended explanations on Computer Science Textbooks

Theory of Computation

Read Explanation

Big Data

Read Explanation

Blockchain Technology

Read Explanation

Computer Programming

Read Explanation

Computer Organisation and Architecture

Read Explanation

Cybersecurity in Computer Science

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.