Can you help me with these proofs 1. Suppose m is an integer. Prove that if m³ is even, then m must be as well.2. Let x = R. Prove that if x is irrational, then I must be irrational too.3. Let y = R. Prove or disprove that if y² is irrational, then y³ is irrational too.

1. Prove that if m3 is even, then m must be even.Proof:We use a proof by contrapositive here. The…

Answered: 1. Suppose m is an integer. Prove that…

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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1. Suppose m is an integer. Prove that if m³ is even, then m must be as well. 2. Let x = R. Prove that if x is irrational, then I must be irrational too. 3. Let y = R. Prove or disprove that if y² is irrational, then y³ is irrational too.