Chapter 3.1, Problem 27E

(a)

To determine

To prove: ~ defines an equivalence relation on A.

(b)

To determine

The equivalence class of $0,\frac{7}{5},\text{ and -}\frac{3}{4}$ for $\text{A=R}$ and $f\left(x\right)=\lfloor x\rfloor$.

(c)

To determine

All the equivalence class when $A=\left\{1,2,3,4,5,6\right\}$ and $f=\left\{\left(1,2\right),\left(2,1\right),\left(3,1\right),\left(4,5\right),\left(5,6\right),\left(6,1\right)\right\}$.