CSCI 301 Homework 3 proof by contradiction Solved

Description

Use the method of proof by contradiction.
1. [4 points] Prove that √6 is irrational.
2. [4 points] If 𝑎, 𝑏 𝜖ℤ , then 𝑎) − 4𝑏 − 2 ≠ 0.

3. [4 points] Suppose Suppose A≠ Ø. Since Ø ⊆A×A, the set R= Ø is a relation on A. Is R
reflexive? Symmetric? Transitive? If a property does not hold, say why.
4. [4 points] Define a relation R on Z as xRy if and only if 4 | (x + 3y)
Prove R is an equivalence relation.
Describe its equivalence classes.