Q41Multiple correct5 Marks10 Jul 2022

Which of the following functions is/are onto (surjective)?

A

$f:\mathbb{N}\to\mathbb{N}$, $f(n)=\begin{cases} n/2,& n\text{ is even}\\ n-1,& \text{otherwise}\end{cases}$.

B

$f:\mathbb{N}\to\mathbb{N}$, $f(n)=\begin{cases} (n+1)/2,& n\text{ is odd}\\ n/2,& \text{otherwise}\end{cases}$.

C

$f:\mathbb{R}\to\mathbb{N}$, $f(n)=\begin{cases}0,& n\in\mathbb{Q}\\1,& \text{otherwise}\end{cases}$.

D

$f:\mathbb{R}\to\mathbb{R}$, $f(n)=n-2$.