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I have to use the above-provided information in the venn diagram to figure out $|C\setminus B\setminus A|$.

I know that \ means the same thing as - (or 'subtraction').

$C = \{1, 8, 13\}$

$B = \{2, 11, 13\}$

$A = \{1, 2, 9, 13\}$

Now, I just have to go in the order that I have written the values of $A$, $B$ and $C$.

First, I have to see what elements are in the $C$ that are not in $B$.

$C - B = \{1, 8\}$ don't include $13$ because $13$ is in $B$ and we are subtracting the common elements.

$\{1, 8\} - A = {8}$

Now that you've seen my process, could you please let me know if this is right or wrong? I attempted this question before and I got 9 as my answer. I don't remember how or why I got that answer, so any help would be greatly appreciated.

amWhy
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seoul_007
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    It's right. And you'll remark that C\A\B = (C\A)\B = (C\B)\A. – math Dec 27 '20 at 16:48
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    I recommend checking very carefully to see what you have been told about the labeling of this diagram. You interpreted the numbers as elements of the universal set and also of the sets in whose circles they appear, but then $13$ is both a member of $A$ and a member of the complement of $A$, which is impossible. I think it is more likely that the numbers represent the number of elements in each region of the graph. – David K Dec 27 '20 at 17:33
  • On your interpretation of the diagram your answer is wrong: ${1,8}\setminus A={8}$, whose cardinality is $1$, not $8$. However, I agree with David K that the numbers are probably the cardinalities of the regions of the diagram, in which case it is true that $|(C\setminus B)\setminus A|=8$. – Brian M. Scott Dec 27 '20 at 21:42
  • Sounds good, thank you! – seoul_007 Dec 28 '20 at 14:24

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