Logout Open In App
Open In App
Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 2: Q2 (page 35)

State the hypothesis and the conclusion of each conditional.

I can’t sleep if I’m not tired.

Short Answer

Expert verified

The hypothesis is I’m not tired and the conclusion is I can’t sleep.

Step by step solution

01

Step 1. Hypothesis and the conclusion.

The hypothesis and the conclusion of a conditional statement is where the hypothesis is the phrase immediately following by the word if and the conclusion is the phrase immediately following by the word then.

02

Step 2. Symbolic representation.

If p represents the hypothesis and q represents the conclusion, then the basic form of an if-then statement is “If p, then q”. For example, in the statement “If today is Friday, then tomorrow is Saturday”, “today is Friday” is the Hypothesis, and “tomorrow is Saturday” is the Conclusion.

03

Step 3. Rewrite the statement.

The given statement “I can’t sleep if I’m not tired” can be rewritten as “If I’m not tired, then I can’t sleep”.

04

Step 4. Identification of Hypothesis and the conclusion.

In the statement “If I’m not tired, then I can’t sleep”, therefore, “I’m not tired” is followed by “If” and “I can’t sleep” is followed by “then” thus, the hypothesis is I’m not tired and the conclusion is I can’t sleep.

Hence, the hypothesis is I’m not tired and the conclusion is I can’t sleep.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

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

If a number is divisible by 6, then it is divisible by 3.

State which postulate, definition, or theorem justifies the statement about the diagram.

m∠AEB+m∠BEC=m∠AEC

Prove the following statement by filling in the blanks.

If A and B have coordinated a and b, with b>a, and the midpoint M of AB¯ has coordinate x, then prove x=a+b2.

Proof:

Statement

Reasons

1. A, M, and B have coordinated a, x, and b respectively; b>a.

1. ?

2. AM=x−a;MB=b−x

2. ?

3. M is the midpoint of AB¯.

3. ?

4. AM¯≅MB¯, orAM=MB

4. ?

5.x−a=b−x

5. ?

6. 2x=?

6. ?

7. x=a+b2

7. ?

Justify each step.

z+73=−11

z+7=−33

z=−40

Copy everything shown and supply missing statements and reasons.

Given:ST=RN;IT=RU

Prove: SI=UN

Proof;
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

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.

Sign-up for free