Venn diagramm: at least one not I have trouble understanding the solution for a venn-diagram exercise our statistics professor gave us. 
The question is:

Of the three events $A, B, C\subset W$ occurs at least one not. Write the
  corresponding event and draw the venn diagram.

The correct solution was:
$(\overline {A\text{ }\cup B\text{ } \cup C}\text{ })$

My solution was:
$(\overline{A\text{ }\cap B\text{ }\cap\text{ }C}\text{ })$

I just can't wrap my head around where I went wrong. If only A, or A and B happens for example, the requirement of one not is still met, isn't it? So the overlap of one or only one should be colored in too. That's at least my thought
 A: The problem seems to be that the formulation "occurs at least one not" could possibly be said to be ambiguous.
Under a very strange reading of the assignment, one could interpret the phrase "at least one not" as "it is not the case that at least one of the events occurs", $\overline{A \cup B \cup C}$, which is equivalent to "none of the events occurs", $\overline{A} \cap \overline{B} \cap \overline{C}$, and thus corresponds to the Venn diagram suggested in the solution.  
However, the more straightforward (and in my judgement, the only acceptable from a grammatical point of view) reading is that "for at least one of the events it holds that it does not occur", $\overline{A} \cup \overline{B} \cup \overline{C}$, equivalently "it is not the case that all of the events occur", $\overline{A \cap B \cap C}$, which corresponds to the situation you correctly pictured in your Venn diagram.
I find it very hard to see that the first reading would be the expected interpretation or even possible at all, and think that your professor should have accepted your solution.
