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Function f from the set of natural numbers to integers defined by 
  • a)
    One-one but not onto
  • b)
    Onto but not one-one
  • c)
    One-one and onto both
  • d)
    Neither one-one nor onto
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Function ffrom the set of natural numbers to integers defined bya)One-...

And f : N → I, where N is the set of natural numbers and I is the set of integers.
Let x, y ∈ N and both are even.

Again, x, y∈ N and both are odd.

⇒ x = y
So, mapping is one-one.
Since, each negative integer is an image of even natural number and positive integer is an image of odd natural number. So, mapping is onto.
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Function ffrom the set of natural numbers to integers defined bya)One-one but not ontob)Onto but not one-onec)One-one and onto bothd)Neither one-one nor ontoCorrect answer is option 'C'. Can you explain this answer?
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