I am having trouble in understanding how to represent the Venn diagram of $C \subseteq A$, $ B \cap C = \varnothing$ because there is no information given about $B \cap A$.

Am I forced to represent the case of each relationship between $A$ and $B$ with a different diagram, i.e., $B \cap A = \varnothing$, $B \cap A \neq \varnothing$, $B \subsetneq A$?

Note that no information about if $A$, $B$ or $C$ are empty or not is given.

  • $\begingroup$ Terminology nit-pick: What you want is not a Venn diagram, but an Euler diagram. Venn diagrams are the special type of Euler diagrams that have no containment relations at all. $\endgroup$ – Arthur Dec 8 '17 at 9:07

It is not possible to know if a discussion of $B\cap A$ is among the untold details of your assignment. Personally, I'd just make two intersecting ellypses for $A$ and $B$ and then I would draw a small circle for $C$ inside the lune that is left in $A$ after cutting away $B$.

  • $\begingroup$ Thank you. There are no untold details of this exercise (it's not an assignment). I am actually giving as much information as possible. And my question still remains - Is there a way to overcome the necessity of representing each different relationship between $A$ and $B$ with a different diagram? You are just ignoring the actual question. $\endgroup$ – Esteban Mendoza Dec 8 '17 at 9:16
  • $\begingroup$ For the informal use I make of Euler-Venn diagrams, drawing a non-empty intersection of two sets does not exclude the fact that the two sets are disjoint. Apparently, strictly speaking this is what drawing a Venn diagram means. If in your context you must strictly draw an Euler diagram, for which disjoint sets cannot have overlapping diagrams, then I presume you must do the three cases (but the presence of $C$ is irrelevant: the problem is in having $A$ and $B$). I would second the former, because it condenses all the relevant information in a concise exposition. $\endgroup$ – user228113 Dec 8 '17 at 9:33

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