(a) Prove that if x is rational and y is irrational, then is irrational. (b) Prove that

Chapter 1, Problem 4

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(a) Prove that if x is rational and y is irrational, then is irrational. (b) Prove that there exist irrational numbers x and y such that isrational.(c) Prove that for every rational number z, there exist irrational numbers xand y such that(d) Prove that for every rational number z and every irrational number x,there exists a unique irrational number y such that

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