I need some help with the second part of this problem. It's from an algebra course.
Let $A$ be the set of all the injective functions $f: \{1,2,3,4\} \rightarrow \{ 1, 2, 3, 4, 5, 6, 7, 8 \}$. The relation $\mathcal R$ in $A$ is define as:
$$f \mathcal R g \iff f(1) + f(2) = g(1) + g(2)$$
First prove that $\mathcal R$ is an equivalence relation. Then if $f \in A$ is the function defined as $f(n) = n+2$. How many elements has its equivalence class.
No problems proving that it's an equivalence relation, but I'm not sure how to think what comes next. Any hints?
I thought about seeing what $f(1)$ and $f(2)$ is if $f(n)=n+2$. So I would end up with $3+4= g(1)+g(2)$. Would that mean that the number of elements in the equivalence class would be the amount of functions $g(1)+g(2)$ that would sum up to 7?
Thanks!