a Prove that this is an equivalence relation b Write down th

(a) Prove that this is an equivalence relation.

(b) Write down the equivalence classes of this relation.

Solution

a)

For any a in R

|a|=|a|

So, R is reflexive

Let, a~b

So, |a|=|b|

Hence, b~a

So, R is symmetric

Let, a~b, b~c

So, |a|=|b|=|c|

Hence, a~c

So, R is transitive and hence equivalence relation

b)

Elements in equivalence class are the pairs: {-a,a} where a is a real number ,a>=0

So uncountably many equivalence classes