Just curious. If the purpose of a proof is to inform and persuade, why don't Venn diagrams count? Is it just convention or is there a more, umm, formal reason haha. Thanks!
Elementary Set Theory – Why Venn Diagrams Don’t Count as Formal Proofs
elementary-set-theoryproof-writing
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Your Venn diagram appears to agree with the statement. As you've noticed (and Srivatsan joked about), a negative number in this context doesn't have a physical interpretation.
Depending on where this question is from, it's possible that the statement is simply wrong. It's also possible that it is meant to say
There are 140 students in a batch. 10 reserved stalls at the spring event and did not play games or sing, 20 sang on the stage and did not reserve a stall or play games, etc.
in which case all of the Venn diagram counts will make sense; but this is not the usual interpretation.
I guess the answer is that this is just a bad question.
Here's what I would do. I hope it answers your question
Best Answer
I don't know exactly what you have written, but I would venture to say that anything you "prove" with Venn diagrams probably has an extremely direct translation into set theory, which would certainly be an acceptable form of proof.
The strongest reason to not let you just use a Venn diagram alone is that your teacher probably wants you to verbalize your explanation. This is a key part of mathematics. Drawing a picture can really help illustrate the idea involved, but it does not always explain the connection to the logic you are working within.
There is also a huge drawback to proving things by Venn diagram: your visual preconceptions may fool you into making a mistake. This cannot happen (or happens to a much smaller degree) when you work in the language of set theory.