For each of the statement below, decide whether it is true or false, and prove your claim. (a) For all a, b ∈ R, if a ∉ Q \ {0} and b ∈ Q then ∉ Q. (b) For all x, y ∈ R, if x is irrational and y is positive and irrational, then x + √y is irrational.
For each of the statement below, decide whether it is true or false, and prove your claim. (a) For all a, b ∈ R, if a ∉ Q \ {0} and b ∈ Q then ∉ Q. (b) For all x, y ∈ R, if x is irrational and y is positive and irrational, then x + √y is irrational.
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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For each of the statement below, decide whether it is true or false, and prove your claim.
(a) For all a, b ∈ R, if a ∉ Q \ {0} and b ∈ Q then ∉ Q.
(b) For all x, y ∈ R, if x is irrational and y is positive and irrational, then x + √y is irrational.
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