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So, my daughter has been given this Venn diagram problem... buuut it's not solvable riiiiight?

enter image description here

Asaf Karagila
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Neilos
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    I neither understand the question, nor the picture. I mean I know what a Venn Diagram is, but for me this is just a bunch of random numbers clamped together. Edit: So you are probably right. Without more context this should not be soluble. – Cornman Feb 02 '22 at 14:35
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    I don't know the context of this venn, but having 49 in the middle and the left immediately makes me suspicious about it. Seems wrong, but only the teacher will know what this is 'supposed' to be! – user2628206 Feb 02 '22 at 14:36
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    What are "headings"? 49 appears in two different regions which is presumably an error. – Matthew Towers Feb 02 '22 at 14:36
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    RHSet: 14+21=35, 14+35=49, 21+35=56,35+49=84, it seems there is a rule. If we add 7 to it we can have 7+14=21. – Mauro ALLEGRANZA Feb 02 '22 at 14:38
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    So the 49s seem an obvious mistake, but even if you remove the 49s it still makes no sense... – Neilos Feb 02 '22 at 14:38
  • My guess for this is, that you should just add random fitting numbers for the ?. So the ? in the intersection could be anything. The questionmark in the left set could be 0, in the right 1. And outside of the set 2 and 3. So there should be infinitly many solutions. You just have to be careful that for exampe the ? outside of the diagram do not appear in the diagram. – Cornman Feb 02 '22 at 14:39
  • And maybe the headings is the cardinality of the set. Where you have to be careful to not count 49 twice, for example. – Cornman Feb 02 '22 at 14:40
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    @Neilos Considering it is a homework for a 9 year old, I would not care to much about the 49 accouring twice. We are not in a highschool class on set theory. (So the question probably does not fit here anyways). – Cornman Feb 02 '22 at 14:42
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    It has something to do with the middle numbers being sums of numbers from the LHS or the RHS. However, it is not clear what the exact rule is. Also, it seems to me that this question is a problem-solving exercise that doesn't really (i.e. shouldn't) have anything to do with sets or Venn diagrams. – Adam Rubinson Feb 02 '22 at 15:01
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    “What’s missing?“ worthwhile pedagogical content in this sheet of paper. – rschwieb Feb 02 '22 at 15:18
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    If anyone is interested in looking at this further, the source for it appears to be: https://blogs.glowscotland.org.uk/dg/public/belmontprimaryredarea/uploads/sites/5227/2020/05/17151815/Problem-Solving-1.pdf – Mitchell Spector Feb 02 '22 at 18:03
  • Maybe consider that the RH set is made of multiples of 7; thus add the missing ones: 7,28,42,63,70,77,91,98, some of which must be "inserted" into the intersection area. – Mauro ALLEGRANZA Feb 03 '22 at 07:53

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Addressing the question on the homework, perhaps the answer is just "no"

Labeling the left circle as $A$ and the right circle as $B$, we note that 49 appears in both $A \cap \bar{B}$ and $A \cap B$ however from set theory

$$(A \cap \bar{B}) \cap (A \cap B) = \bar{B} \cap B=\phi$$

So we should expect the empty set but since we see 49, that's a contradiction.

Julie Taylor
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