/*! 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} Problem 26 Write the converse, inverse, and... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 26

Write the converse, inverse, and contrapositive of each statement. If the review session is successful, then no students fail the test.

Short Answer

Expert verified
Converse: 'If no students fail the test, then the review session is successful.' Inverse: 'If the review session is not successful, then some students fail the test.' Contrapositive: 'If some students fail the test, then the review session is not successful.'

Step by step solution

01

Identify the Hypothesis and Conclusion

In any conditional statement, the two important parts are the hypothesis and the conclusion denoted 'if P then Q'. In the given problem, the phrase 'If the review session is successful' is the hypothesis (P) and 'no students fail the test' is the conclusion (Q).
02

Write the Converse

The converse of a statement is formed by interchanging the hypothesis and the conclusion. So, the converse of the given statement is 'If no students fail the test, then the review session is successful.'
03

Write the Inverse

The inverse of a statement is formed by negating both the hypothesis and the conclusion. So, the inverse of the given statement is 'If the review session is not successful, then some students fail the test.'
04

Write the Contrapositive

The contrapositive of a statement is formed by interchanging and negating both the hypothesis and the conclusion. So, the contrapositive of the given statement is 'If some students fail the test, then the review session is not successful.'

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

Use the standard forms of valid arguments to draw a valid conclusion from the given premises. If all houses meet the hurricane code, then none of them are destroyed by a category 4 hurricane. Some houses were destroyed by Andrew, a category 4 hurricane. Therefore, ...

Use Euler diagrams to determine whether each argument is valid or invalid. All writers appreciate language. All poets are writers. Therefore, all poets appreciate language.

Use the standard forms of valid arguments to draw a valid conclusion from the given premises. You exercise or you do not feel energized. I do not exercise. Therefore, ...

Use the standard forms of valid arguments to draw a valid conclusion from the given premises. If the Westway Expressway is not in operation, automobile traffic makes the East Side Highway look like a parking lot. On June 2, the Westway Expressway was completely shut down because of an overturned truck. Therefore, ...

If you are given an argument in words that contains two premises and a conclusion, describe how to determine if the argument is valid or invalid.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Probability and 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.