Prove the following statements using contradiction. Please do them on a separate sheet of paper, separate from your notes. (1) Let a and b be real numbers where a is rational and ab is irra- tional. Show that b is irrational. (a) Scratchwork: (b) Proof:

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter7: Real And Complex Numbers
Section7.1: The Field Of Real Numbers
Problem 20E: Give counterexamples for the following statements. If and are irrational, then is irrational. If ...
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Prove the following statements using contradiction. Please do them
on a separate sheet of paper, separate from your notes.
(1) Let a and b be real numbers where a is rational and ab is irra-
tional. Show that b is irrational.
(a) Scratchwork:
(b) Proof:
Transcribed Image Text:Prove the following statements using contradiction. Please do them on a separate sheet of paper, separate from your notes. (1) Let a and b be real numbers where a is rational and ab is irra- tional. Show that b is irrational. (a) Scratchwork: (b) Proof:
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