We know the general figure of Venn diagrams for two or three distinct sets.
There are many formulas related to two or three sets.
For example, one of Distributive Law is
$$A \cup (B \cap C) = (A \cup B) \cap (A \cup C).$$
We can visualize it by using Venn Diagram, and guess that it is true.
And also, we can prove it to show that each side is contained in the other side.
It is my question. For rigorous proof, I know we should only use mathematical logic and theorem. Nonetheless, I want to check that Venn Diagram proof is also available for some easier cases.
Can Venn Diagram be one method of proof?
Can we prove that all proof by using Venn Diagram method for two or three sets is true?
If we prove that, then all statements for two or three sets can be strictly proved by using Venn Diagram.