Answer:
Step-by-step explanation:
Let f be a function from N to N.
N_set of all natural numbers
i) one to one but not onto
consider the function
[tex]f(x) = x^2[/tex]
When two numbers have same square we find that the numbers should be the same because they are positive.
So one to one but not onto because consider 3 it does not have square root in N.
ii) Onto but not one to one
Consider
[tex]f(x) = x, x odd\\f(x) = x/2, x even.[/tex]
this is onto because every number has a preimage in N.
But not onto because consider 6 and 3, f(6) = 3 and f(3) =3
So not one to one
iii) both onto and one-to-one
f(x) = [tex]\\\\x-1,x odd[/tex]
=x+1, x even
This is both one to one and onto since we consider only integers
iv) Neither one to one nor onto
Consider the function
f(x) = 2
This is not onto because 3 cannot have a preimage in N, not one to one because f(1) = f(2) where 1 not equals 2
