There is one-one correspondence between the elements of the set A and the set B.
2. Many-one function
There is many-one correspondence between the elements of the set A and the set B.
3. Onto function
Every element of the set B has at least one pre-image.
In above fig.(i), the function is one-one and onto, while in fig.(ii) the function is many-one and onto.
4. Into function
There is at least one element of B which has no pre-image.
In above fig.(i) the function is one-one and into, while in fig.(ii) the function is many-one and into.
For types of functions, the four arrow diagrams given for one-one and many-one are repeated for ONTO and INTO functions because each function is always one-one onto or one-one into; many-one onto or many-one into.
