/*! 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} Q19. What simpler name can be used fo... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q19. (page 212)

What simpler name can be used for the converse of the inverse of a conditional?

Short Answer

Expert verified

The converse of the inverse of a conditional statement is Contrapositive.

Step by step solution

01

Step 1. Define contrapositive, inverse, and converse for the given statement

If the given statement is 鈥樷�橧f p then q鈥欌��, the contrapositive is 鈥樷�橧f not q then not p鈥欌赌�.

If the given statement is 鈥樷�橧f p then q鈥欌��, the converse is 鈥樷�橧f q then p鈥欌赌�.

If the given statement is 鈥樷�橧f p then q鈥欌��, the inverse is 鈥樷�橧f not p then not q鈥欌赌�.

02

Step 2. Let a conditional

Consider conditional statement is p鈫�q.

Then define inverse statement for conditional:

Inverse statement of p鈫�qis ~p鈫�~q
.

Define converse of the conditional:

The converse of the statement ~p鈫�~qis ~q鈫�~p.

03

Step 3. Check the converse of the inverse of conditional

From the definition of contrapositive, define contrapositive of conditional as:~q鈫�~p

Hence, the converse of the inverse of a conditional statement is Contrapositive.

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

Two sides of a triangles have length 15 and 20. The length of the third side can be any number between __ and __?

Prove that the diagonals of a trapezoid do not bisect each other.

Complete the following statement with the word always, sometimes, or never.

Two lines parallel to the same plane _____ intersect.

Prove that if two angles of a triangle are not congruent, then the sides opposite those angles are not congruent.

A certain conditional is true. Must its converse be true? Must its inverse be true? Must its contrapositive be true?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

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.