Question

The function f: N → N, where

f(n) = `{{:(1/2(n + 1), "If n is sold"),(1/2n, "if n is even"):}` is

Options

• one - one

• many - one

• one - one onto

• many - one onto

Answer 1

many - one onto

Explanation:

For one - one

`f(1) = 1/2(1 + 1)` = 1

`f(2) = 1/2 xx 2` = 1

∴ `f(n)` is not one-one. (i.e., mant - one)

For onto

If n is odd

Let `y = 1/2 (n + 1)` ⇒ `n = 2y - 1`.

n is odd for y ∈ N.

If n is even

Let `y = 1/2 n` ⇒ `n = 2y`,

n is even for y ∈ N.

∴ Range = N = Codomain

So, `f(n)` is onto.