Prove the following using the specified technique: (a) Let a and y be two real numbers such that r +y is rational. Prove by contrapositive that if t is irrational, then a – y is irrational. (b) Prove by contradiction that for any positive two real numbers, x and y, if r y< 50, then either z < 8 or y < 8.

Prove the following using the specified technique: (a) Let a and y be two real numbers such that r +y is rational. Prove by contrapositive that if t is irrational, then a – y is irrational. (b) Prove by contradiction that for any positive two real numbers, x and y, if r y< 50, then either z < 8 or y < 8.

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Description: Am I starting these proofs correctly? Please let me know what the next step should be I can't figure out what to do next. Prove the following using the specified technique:(a) Let x and y be two real numbers such that r+y is rational, Prove by contra

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 13E: 13. Prove that if and are rational numbers such that then there exists a rational number such...

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Am I starting these proofs correctly? Please let me know what the next step should be I can't figure out what to do next.

Prove the following using the specified technique:
(a) Let x and y be two real numbers such that r+y is rational, Prove by contrapositive tlhat if
is irrational, then x – y is irrational.
(b) Prove by contradiction that for any positive two real numbers, ¤ and y, if x · y < 50, then
either x < 8 or y < 8.
a) Praof:
Let X and
is riational's Assume That if X is (ational, then
X-y is
yi O and re.
be two real nnmbrs such that Xty
rational. A numbor r is rational if
メ
b) Prosf:
Assume that
if x.y 550 Then
メ28 or y28
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