Chapter 7: Problem 17
Prove the following statements. These exercises are cumulative, covering all techniques addressed in Chapters \(4-7\). There is a prime number between 90 and 100 .
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Prove the following statements. These exercises are cumulative, covering all techniques addressed in Chapters \(4-7\). Suppose \(a, b \in \mathbb{Z} .\) Prove that \((a-3) b^{2}\) is even if and only if \(a\) is odd or \(b\) is even.
Prove the following statements. These exercises are cumulative, covering all techniques addressed in Chapters \(4-7\). Suppose \(x, y \in \mathbb{R} .\) Then \(x^{3}+x^{2} y=y^{2}+x y\) if and only if \(y=x^{2}\) or \(y=-x\).
Prove the following statements. These exercises are cumulative, covering all techniques addressed in Chapters \(4-7\). Suppose \(a, b \in \mathbb{Z}\). Prove that \(a \equiv b(\bmod 10)\) if and only if \(a \equiv b(\bmod 2)\) and \(a \equiv b\) \((\bmod 5)\).
Prove the following statements. These exercises are cumulative, covering all techniques addressed in Chapters \(4-7\). Suppose \(x, y \in \mathbb{R}\). Then \((x+y)^{2}=x^{2}+y^{2}\) if and only if \(x=0\) or \(y=0\).
Prove the following statements. These exercises are cumulative, covering all techniques addressed in Chapters \(4-7\). Every real solution of \(x^{3}+x+3=0\) is irrational.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
