4 For each of the following relations determine whether it i

4. For each of the following relations, determine whether it is reflexive, symmetric, or transitive. For those that are equivalence relations, give the equivalence classes.

Solution

1. f(a)=f(a)

So, aRa and hence R is reflexive

2. Let, aRb

So, f(a)=f(b) hence, bRa

So, R is symmetric

3. Let, aRb and bRc

SO, f(a)=f(b), f(b)=f(c)

f(a)=f(c)

So, aRc

Hence, R is transitive

So, R is equivalence relation

An equivalence class would be

For each, a in A {b: f(b)=f(a), b in A}

THis will give us all the equivalence clases