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

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.

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(b) List the elements in the equivalence class E(9, 2).

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

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

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

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(f) Let B = ×  and extend R to an equivalence relation on B. Now what does E(9. 2) look like?