Listing all elements of a set I was given a question like the following:

Let $A = \Bbb Z$, $B = [-1,\pi]$ , $C=(2,7)$. List all Elements of $A \cap (B^c \cap C)$.

I do not really understand how to got about this problem. I understand $\cap$ means intersection, but I have trouble reading the question; for instance, why place brackets between $B^c \cap C$?
 A: I am going to assume that your domain of discourse is the real numbers $\mathbb{R}$. To that end, structure your computations like so to facilitate an easily produced answer:


*

*$B^c = (-\infty,-1)\cup(\pi,\infty)$ 

*$B^c\cap C=(\pi,7)$

*$A\cap(B^c\cap C)=\{4,5,6\}$


This way of going about it is just one way of doing it though. Since $\cap$ is associative, you could computer the intersections of $A$ and $B^c$ first or you could use a variety of other set identities. But the method above is probably the most natural and easiest. 
A: We have $A=\mathbb Z, B=[-1,\pi],C=(2,7)$, thus we obtain $B^c=\mathbb R\setminus C=(-\infty,-1)\cup (\pi,\infty)$. As $3<\pi<4$ we have $B^c\cap C=(\pi,7)$. The only integers in $(\pi,7)$ are given by $4,5,6$ so we conclude: $A\cap(B^c\cap C)=\{4,5,6\}$.
On the use of brackets: intersection is an associative operation, so one could ignore the brackets and just write $A\cap B^c\cap C$; as intersection is also commutative we can change the order e.g. look at $A\cap B^c\cap C= B^c\cap A\cap C$. This gives us the opportunity to compute the intersection of two sets that feels the easiest; the brackets given in the question already give you a nice order of computing.
