Hi Masters.

With all due respect, could you give me a hint for the questions?

1. Let X = {1, 2, 3, 4, 5} and Y = {3, 4}. Define a relation R on the power set P(X)

of X by A R B iff A union Y = B union Y

(a) Prove that R is an equivalence relation.

(b) What is the equivalence class of {1, 2}?

2. Let X be Z * Z, i.e. X is the set of all ordered pairs of the form (x, y) with x, y is an element of Z.

Define the relation R on X as follows:

(x1, x2)R(y1, y2) iff x1^2 + x2^2 = y1^2 + y2^2

Is it an equivalence relation?

Have a great day, masters!