Let A = × , and define a relation R on A by (a, b) R (c, d ) iff ab = cd. (a) Show that R is an equivalence relation on A. (b) List the elements in the equivalence class E(9, 2). (c) Find an...

Let A =

×
, and define a relation R on A by (a, b) R (c, d ) iff ab = cd.

(a) Show that R is an equivalence relation on A.

(b) List the elements in the equivalence class E_{(9, 2)}.

(c) Find an equivalence class with exactly two elements.

(d) Find an equivalence class with exactly three elements.

(e) Find an equivalence class with exactly four elements.

(f ) Let B =

×

and extend R to an equivalence relation on B. Now what does E_{(9, 2)}
look like?