Question

Problem 13.5. Consider a “square” S = {(x, y) : x, y ∈ {−2, −1, 0, 1, 2}}. (a) Let (x, y) ∼ (x 0 , y0 ) iff |x| + |y| = |x 0 | + |y 0 |. It is an equivalence relation on S. (You don’t need to prove it.) Write the elements of S/ ∼. (b) Let (x, y) ∼ (x 0 , y0 ) iff • x and x 0 have the same sign (both positive, both negative, or both 0), and • y and y 0 have the same sign (defined as above). It is an equivalence relation on S. (You don’t need to prove it.) Write the elements of S/ ∼.

Answer 1