- #1

davon806

- 148

- 1

## Homework Statement

Hi,I am stuck on my maths assignment.

Describe equivalence classes for the following equivalence relations on the given set S.

(i) S = R, and a ∼ b ⇐⇒ a = b or −b.

(iii) S = R, and a ∼ b ⇐⇒ a^2 + a = b^2 + b.

(v) S is the set of all points in the plane, and a ∼ b means a and b are the same distance from the origin. (vi) S = N, and a ∼ b ⇐⇒ ab is a square.

(viii) S = R × R, and (x, y) ∼ (a, b) ⇐⇒ x^2 + y^2 = a^2 + b^2 .

## Homework Equations

## The Attempt at a Solution

I am asking because I don't know what does an equivalence class mean.

For example,in (i) given a is equal to b or -b.So what do I need to answer?I have been searching for some solved examples but I am still fail to understand.Which one is the variable?a or b?If b is fixed then a must be equal to b or -b to satisfy the relation.But then what do I need to show?

For (v),the equivalence class is the set of solution lies on the circle of radius a,but again what do I need to show?I don't know what to do with the b.

Thanks