Composition/Double names/Permutation of names/Exercise

Let ${}M$ be the set of all female compound first names (names of the form ${}A-B$, where ${}A,B$ are simple first names and every combination is allowed). We consider the composition

$M\times M\longrightarrow M$

which sends a pair of double first names ${}(A-B,C-D)$ to the double name ${}A-D$.

1. What is the value of ${}({\text{Lea-Marie}},{\text{Klara-Sophie}})$ under this composition?
2. Is this composition commutative?
3. Is this composition associative?
4. Does this composition have a neutral element?
5. Is this composition surjective?
6. Is this composition injective?

Create a solution