Let f : N → N be defined by f(n) = n − 1 if n is even, and f(n) = n + 1 if n is odd. Then f is:

Let f : N → N be defined by f(n) = n − 1 if n is even, and f(n) = n + 1 if n is odd. Then f is:

• A. one-one but not onto
• B. onto but not one-one
• C. bijective
• D. neither one-one nor onto

Answer: C) bijective

Explanation: f(1) = 2, f(2) = 1, f(3) = 4, f(4) = 3, etc. f is its own inverse, so it is bijective. (f∘f)(n) = n for all n.