This is probably something very obvious, but I am a little confused. It's about the associative law.
It is known that a binary structure $(S, *)$ is associative if:
$(a * b) *c = a * (b * c)$ for all elements in $S$. It's also closed, as well.
Well, say I wanted to do this with for elements in the set: $\{a,b,c,d\}$. Would parenthesizing for the associative law go something like this?
$(a * b) * c * d = a * b * (c * d) = a * (b * c) * d$ .....etc.
I know the gist of the law states that it doesn't matter which two elements you enact the operation with first, it will always be the same. But for understanding and a hw exercise, I need to know if I'm going about this correctly.