Give an example of a function from N to N that is
a) one-to-one but not onto.
b) onto but not one-to-one.
c) both onto and one-to-one (but different from the identity function).
d) neither one-to-one nor onto.
We have to find the example of a function from, set of natural numbers to set of natural numbers that is,
a)One-one but not onto
This function is one - one.
But this is not onto because zero is not in the image.
b)Onto but not one-one
Therefore the function is not one-one.
But this function is onto ,because for every element in the codomain has at least one preimage.
f(x+1) = x.