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Let S = {a , b , c}" and "T = {1, 2, 3}....

Let `S = {a , b , c}" and "T = {1, 2, 3}`. Find `F^(-1)` of the following functions F from S to T, if it exists.
(i) `F = {(a , 3), (b , 2), (c , 1)}`
(ii) `F = {(a , 2), (b , 1), (c , 1)}`

Text Solution

Verified by Experts

The correct Answer is:
(i) `F^(-1) = {(3, a), (2, b), (1, c)}`
(ii) `F^(-1)` does not exists.
`S = {a , b , c}" and "T = {1, 2, 3}`.
(i) `F: S -> T` is defined by `F = {(a , 3), (b , 2), (c , 1)}`
`implies F(a) = 3, F(b) = 2, F(c) = 1`
Thus, `F^(-1): T -> S` is given by `F^(-1) = {(3, a), (2, b), (1, c)}`.

(ii) `F: S -> T` is defined by `F = {(a , 2), (b , 1), (c , 1)}`
`implies F(b) = F(c) = 1`, F is not one-one.
Hence, `F` is not invertible i.e., `F^(-1)` does not exists.
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