If `A={1,\ 2,\ 3,\ 4}` and `B={a ,\ b ,\ c ,\ d}` . Define any four bijectives from `A` to `B` . Also, give their inverse functions.

Explanation

`f_{1}={(1, a),(2, b),(3, c),(4, d)} Rightarrow f_{1}^{-1}={(a, 1),(b, 2),(c, 3),(d, 4)} `


`f_{2}={(1, b),(2, a),(3, c),(4, d)} Rightarrow f_{2}^{-1}{(b, 1),(a, 2),(c, 3),(d, 4)} `


`f_{3}={(1, a),(2, b),(4, c),(3, d)} Rightarrow f_{3}^{-1}{(a, 1),(b, 2),(c, 4),(d, 3)} `


`f_{4}={(1, b),(2, a),(4, c),(3, d)} Rightarrow f_{4}^{-1}={(b, 1),(a, 2),(c, 4),(d, 3)}`



Clearly, all these are bijections because they are one-one and onto.