Consider the set of all functions $f:\{0,1, \dots,2014\} \to \{0,1,\dots, 2014\}$ such that $ f\left(f\left(i\right)\right)=i$, for all $0 \leq i \leq 2014$. Consider the following statements:
$P$. For each such function it must be the case that for every $i,f(i) = i$.
$Q$. For each such function it must be the case that for some $i,f(i)=i$.
$R$. Each function must be onto.
Which one of the following is CORRECT?
- $P, Q$ and $R$ are true
- Only $Q$ and $R$ are true
- Only $P$ and $Q$ are true
- Only $R$ is true