Answered: Theorem: For any real number x, if (x -…

Theorem: For any real number x, if (x - 1)(x + 5) <0 then - 5 < x < 1 Suppose that the theorem is proven by contrapositive, so the proof starts by assuming that it is not the case that - 5

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Theorem: For any real number x, if (x - 1)(x+5) <0
then - 5 < x < 1
Suppose that the theorem is proven by contrapositive, so the proof starts by assuming that it is not the case that - 5 <x< 1
and then shows that (x - 1)(x+5) ²0
What are the two cases that cover the set of x in the assumption?
O a. Case 1: x 2-5, Case 2: x ≥ 1
O b. Case 1: x2-5, Case 2: x ≤ 1
O c. Case 1: x ≤-5, Case 2: x
1
d. Case 1: x ≤-5, Case 2: x ≤ 1

Expert Solution

Step 1

Introduction:

The contrapositive of "if A then B" is a proposition or theorem that is generated by opposing both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem and exchanging them.

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