/*! 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} Q14 Provide a counterexample to show... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q14 (page 35)

Provide a counterexample to show that each statement is false.

Statement: If xy>5y, than x>5.

Short Answer

Expert verified

The counterexample, x=3and y=鈭�6, shows that the statement is false.

Step by step solution

01

Step 1. Define counterexample.

The counterexample is an example for which a hypothesis is true but the conclusion is false for an if-then statement.

02

Step 2. State the counterexample

In order to show, 鈥淚f xy>5y, then x>5.鈥� is false letx=3 andy=鈭�6.

03

Step 3. Verify the counterexample.

If x=3and y=鈭�6, then

xy=3鈭�6=鈭�18

and,

5y=5脳鈭�6=鈭�30

Since, 鈭�18>鈭�30, hence xy>5y. But, x=3<5, thus, x<5,which contradicts the inequality.

Therefore, the counterexample, x=3and y=鈭�6, shows that the statement is false.

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

Justify each statement with a property from algebra or property of congruence.

2a+b=2a+2b

State the hypothesis and the conclusion of each conditional.

If she鈥檚 smart, then I鈥檓 a genius.

State the hypothesis and the conclusion of each conditional.

Combine the conditionals in Exercises 5 and 6 into a single biconditional.

State the converse of each conditional. Is the converse true or false?

If , then .

Copy everything shown and write a two-column proof.

Given:m鈭�SRT=m鈭�STR;

m鈭�3=m鈭�4

Proof:m鈭�1=m鈭�2
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Decision Maths

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.