Let A=Q×Q, where Q is the set of all rational numbers, and * be a bin

1.	Let A=Q×Q, where Q is the set of all rational numbers, and * be a binary operation on A defined by (a, b) * (c, d) = (ac, b + ad) for (a.b),(c,d)ϵA. Then find (i) The identity element of * in A. (ii) Invertible elements of A, and hence write the inverse of elements (5, 3) and. (12,4). OR Let f : W→W be defined as f(n){n−1,if n is oddn+1,if n is even Show that f is invertible and find the inverse of f. Here, W is the set of all whole numbers.
Answer» Let $A = Q \times Q$ , where Q is the set of all rational numbers, and * be a binary operation on A defined by (a, b) * (c, d) = (ac, b + ad) for $(a . b), (c, d) ϵ A$ . Then find (i) The identity element of * in A. (ii) Invertible elements of A, and hence write the inverse of elements (5, 3) and. $(\frac{1}{2}, 4)$ . OR Let f : $W \to W$ be defined as $f (n) {\begin{matrix} n - 1, & if n is odd n + 1, & if n is even \end{matrix}$ Show that f is invertible and find the inverse of f. Here, W is the set of all whole numbers.

Let A=Q×Q, where Q is the set of all rational numbers, and * be a binary operation on A defined by (a, b) * (c, d) = (ac, b + ad) for (a.b),(c,d)ϵA. Then find (i) The identity element of * in A. (ii) Invertible elements of A, and hence write the inverse of elements (5, 3) and. (12,4). OR Let f : W→W be defined as f(n){n−1,if n is oddn+1,if n is even Show that f is invertible and find the inverse of f. Here, W is the set of all whole numbers.

Answer»

Let $A = Q \times Q$ , where Q is the set of all rational numbers, and * be a binary operation on A defined by (a, b) * (c, d) = (ac, b + ad) for $(a . b), (c, d) ϵ A$ . Then find

(i) The identity element of * in A.

(ii) Invertible elements of A, and hence write the inverse of elements (5, 3) and. $(\frac{1}{2}, 4)$ .

Let f : $W \to W$ be defined as

$f (n) {\begin{matrix} n - 1, & if n is odd n + 1, & if n is even \end{matrix}$
Show that f is invertible and find the inverse of f. Here, W is the set of all whole numbers.

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