Divide.
2 answers:
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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
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
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) =
=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