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.

Step 1</p>

We have to find the example of a function from, set of natural numbers to set of natural numbers that is,

Step 2</p>

a)One-one but not onto

Consider function

.

This function is one - one.

But this is not onto because zero is not in the image.

Step 3</p>

b)Onto but not one-one

Clearly

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.