Is there a better way to understand set operation

In measure theory, for example, we always need to find a good way to express a set to show its measurability. eg: we write $ A cap B$ as

$$ A cap B = Dbackslash( (Dbackslash A) cup (Dbackslash B) ). $$ to show $ A cap B$ is Jordan measurable.

So, I have two question:

1. How to get the result of set operation faster (is real number operation an analogy of set operation)? Is there any other trick of set algebra?

2. How to construct the set relationship?