## Description

Use the method of proof by contradiction.

1. [4 points] Prove that √6 is irrational.

2. [4 points] If �, � �ℤ , then �) − 4� − 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.