Let `S = {a , b , c} a n d 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)}`

Explanation

S = {a, b, c} and T = {1, 2, 3}
(i) `F : S rarr T`
and F= {(a, 3) , (b, 2), (c, 1)} ⇒ F(a) = 3, F(b) = 2, F(c) = 1 `:. ` Fis one-one onto
`rArr F^(-1): T rarr s `
and `F^(-1)` = {(3, a) , (2, b) , (1, c)}
(ii) `F: S rarr T`
and F = {(a, 2), (b, 1) , (c, l)}
`therefore F(a) = 2, F(b) = 1, F(c) = 1`
`because` F(b) = F(c)
and ` b ne c`
`therefore ` F is not one-one
`rArr F^(-1)` does not exist