I am trying to understand PRF's and PRP's. I have got a question where I have to decide whether $F(k,x) = (k \wedge x ) \oplus k$ (where $k$ and $x$ are simple $1$ bits (1 or 0)) is PRP or not. I am not sure if I understand PRP's correctly. As I have found:
A Pseudo Random Permutation is a PRF that happens to have the property that every element in the input domain has a single associated member in the output co-domain and vice versa.
So what I have got in my example.
k x F(k,x) 0 0 0 0 1 0 1 0 1 1 1 0
For each couple, I have an associated member in output co-domain, but for each output 0 and 1. I do not have a unique member in the input domain. So this function is not PRP. Am I right?