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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.

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    You should explore with drawing some simple cases. Take $A,B,C,D$ to be intervals, and consider the various cases ($A$ and $C$ disjoint, $A$ and $C$ nested, and $A$ and $C$ meeting but not nested; ditto with $B$ and $D$). If you don't develop graphical intuition, you will be hampered in many ways later on. – 2017-01-27

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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).