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(i) ƒ : {1,2,3,4} → {5} defined by ƒ = {(1,5), (2,5), (3,5), (4,5)} Does the function is invertible?

(ii) Let A = Nx N, N-set of natural numbers and * 1be a binary operation on A defined by (a,b) * (c,d) = (ac—bd,ud +bc). Show that* is commutative on A.

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(i) Inverse does not exists because fis not one-one.

(ii)  Given (a,b)*(c,d) = (ac - bd, ad + bc)

(c,d) * (a,b) = (ca - db, cb + da)

= (ac - bd, ad + bc)

= (a,b )*(c,d)

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