I want to give my students some example problems for proving set equality about why you cannot take the general venn diagram proof at face value. I read this post that stated venn diagrams are not formal proofs.
Assume that students are using the basic idea of two partially overlapping circles (because that is the most common version students know).
In this case an identity that would fit the bill is one that does not work when either $A=B$, $A\cap B=\varnothing$ or $A\subset B$.
Any thoughts?
Best Answer
$A \cap (B\times C)=(A\cap B) \times (A \cap C)$. I don't really know how you can represent the Cartesian product with Venn diagrams. So any set identity involving them would work.
I would think introducing infinite set operations would render Venn diagrams useless. Very often in math you have a series of sets $\{A_k\}_{k=1}^\infty$ and you want to find $\bigcap_{k=1}^\infty A_k$