discrete mathematics - Showing a counter-example for a 4 sets that share a subset relation

What is the easiest and correct way of finding a counter-example of this kind of questions:

Do these relation holds for every sets $A,B,C,D$?

1) $ (A \setminus C) \times (B \setminus D)) = (A \times B)\setminus(C
\times D) $

2) $ (C \times D) \setminus (A \times (D \setminus B)) \subset (A
\times D) \cup (C \times (D \setminus B)) $

Thanks in advance.

Answer

Here's my answer to the actual question you asked, not the specific set theory questions.

For me the "easiest and correct way" to decide whether such a statement is true is to play with small examples. That often leads either to a counterexample (if the assertion is false) or to an idea of how to prove it (if it's true).