Consider the following statement. For all positive real numbers r and s, Vr+s * VT + Vs. Construct a proof by contradiction for the statement by selecting sentences from the following scrambled list and putting them in the correct order. By the zero product property, at least one of yr or Vs equals 0, which implies that r or s equals 0. Simplifying the equation gives that 0 = 2rs. Squaring both sides of the equation gives that r+s = r+ 2/rvs + s. By the zero product property, at least one of r or s equals 0. But this is a contradiction because r and s are positive. Squaring both sides of the equation gives that r+ s =r+ 2rs + s. Simplifying the equation gives that 0 = 2/rvs. Proof by contradiction: 1. Suppose not. That is, suppose there exists positive real numbers r and s such that Vr+ s = Vr + Vs. 2. ---Select-- 3. --Select-- 4. ---Select--- 5. ---Select--- 6. Thus, we have reached a contradiction and have proved the statement.

Consider the following statement. For all positive real numbers r and s, Vr+s * VT + Vs. Construct a proof by contradiction for the statement by selecting sentences from the following scrambled list and putting them in the correct order. By the zero product property, at least one of yr or Vs equals 0, which implies that r or s equals 0. Simplifying the equation gives that 0 = 2rs. Squaring both sides of the equation gives that r+s = r+ 2/rvs + s. By the zero product property, at least one of r or s equals 0. But this is a contradiction because r and s are positive. Squaring both sides of the equation gives that r+ s =r+ 2rs + s. Simplifying the equation gives that 0 = 2/rvs. Proof by contradiction: 1. Suppose not. That is, suppose there exists positive real numbers r and s such that Vr+ s = Vr + Vs. 2. ---Select-- 3. --Select-- 4. ---Select--- 5. ---Select--- 6. Thus, we have reached a contradiction and have proved the statement.

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

Construct a proof by contradiction for the statement by selecting sentences from the following scrambled list and putting them in the correct order.

Consider the following statement.
For all positive real numbers r and s, Vr+s * VT + Vs.
Construct a proof by contradiction for the statement by selecting sentences from the following scrambled list and putting them in the correct order.
By the zero product property, at least one of yr or Vs equals 0, which implies that r or s equals 0.
Simplifying the equation gives that 0 = 2rs.
Squaring both sides of the equation gives that r+s = r+ 2/rvs + s.
By the zero product property, at least one of r or s equals 0.
But this is a contradiction because r and s are positive.
Squaring both sides of the equation gives that r+ s =r+ 2rs + s.
Simplifying the equation gives that 0 = 2/rvs.
Proof by contradiction:
1. Suppose not. That is, suppose there exists positive real numbers r and s such that Vr+ s = Vr + Vs.
2. ---Select--
3. --Select--
4. ---Select---
5. ---Select---
6. Thus, we have reached a contradiction and have proved the statement.

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