Question 1189006: Please explain how a. Vi and b. i and ii work.
https://docs.google.com/document/d/1ELpsYiSz9SEXTm8wbhrc8E2lS_mr2YME6ihRbBIhlMo/edit?usp=sharing
Found 2 solutions by greenestamps, Solver92311:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
(a)(vi): n(U) is the number in the universal set, which is everything in the diagram:
(2a)+(a)+(a+4)+(a-5) = 5a-1
(b)(i): Use the result from (a)(vi)
5a-1=29
Solve using basic algebra....
(b)(ii): Likewise....
But this time the numbers turn out not to be whole numbers -- which means this case is not possible.
Answer by Solver92311(821)  (Show Source):
You can put this solution on YOUR website!
 .
A.vi: ) means the cardinality of the Universal set, which is the total number of elements in the entire Venn diagram.
There are  elements that are in set  that are not in set  ,  elements that are in  ,  elements in that are not in , and  elements that are not in either or .
Therefore \ =\ 2a\ +\ a\ +\ a\ +\ 4\ +\ a\ -\ 5\ =\ 5a\ -\ 1)
B.i. If \ =\ 29) , then  and so  .
ii. If \ =\ 31) , then  and  . Hence, this is an invalid answer because any cardinality must be a non-negative integer. Therefore, is impossible.
John
My calculator said it, I believe it, that settles it
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