/*! 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} Q10 Provide a counterexample to show... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q10 (page 34)

Provide a counterexample to show that each statement is false. You may use words or draw a diagram.

If a number is divisible by 4, then it is divisible by 6.

Short Answer

Expert verified

The counterexample is number 16.

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. Observation of the statement.

In order to find a counterexample for the statement 鈥淚f a number is divisible by 4, then it is divisible by 6.鈥� we need to find a number that is divisible by 4 but not 6.

03

Step 3. State the counterexample.

Consider the number 16 which is divisible by 4. But clearly, 16 is not divisible by 6. Thus, the statement becomes false.

Therefore, the number 16 is a counterexample.

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

Provide a counterexample to show that each statement is false.

Statement: If point G is on AB鈫�,then G is onBA鈫�.

Can you conclude from the information given for the exercise that XY鈫�鈯�XZ鈫�?

鈭�1and鈭�3 are complementary.

You are told that the measure of an acute angle is equal to the difference between the measure of a supplement of the angle and twice the measure of a complement of the angle. What can you deduce about the angle? Explain.

Use the conditional: If AB炉and CD炉intersect, then AB鈫�and CD鈫�intersect.

Write the converse of the conditional. Is the converse true or false?

In the diagram, DE炉鈯�n. Sate the theorem or name the definition that justifies the statement about the diagram.

鈭�9 and 鈭�10 are complementary.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Logic and Functions

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.