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Math homework question

My teacher shows this in the class but I dont understand it. Is it ok if experts can explain this question? I donot understand how it calculate the B'? According to my calculation B'={2,4,6,8,12,14,16,18,22,24,26,28,32,34,36,38,42,44,46,48,52,54,56,58,62,64,66,68,72,74,76,78,82,84,86,88,92,94,96,98} but in the book it solves B'=6

Tommy Anderson
Tommy Anderson
2 Solutions
Shaun KlineLead Software EngineerCommented:
If I understand the notation being used, B' is the complement of B. So you are correct in that B' is all of the positive integers not divisible by 5 up to and including 100.

However, the solution is using a shorthand approach to solve n ( A intersect B' ) by understanding that this is asking for the number of elements in A that are not in B.

Since you already determined that there are 6 elements in both A and B, then the number of elements that are just in A is 33 - 6.
ste5anSenior DeveloperCommented:
How are A' and B' defined?
I am afraid you are missing quite a lot:

A = { 3, 6, 9, ... , 99)    
A' = { 1, 2, 4, 5, 7, ... 100}  <== everything that is not in A

B =  {5, 10, 15, ... 100}
B' = { 1, 2, 3, 4, 6, 7, ... 99}  <== everything that is not in B

n( B) = 20  <== The number of elements in B not the elements themselves.
n( B') = 80  ==>  The number of elements in U minus the number of elements in B

Your answer   B' = { 2, 4, 6, 8, 12, ... , 98}  does not make sense for this problem.
There is now mention of even (or odd) numbers.
Tommy AndersonAuthor Commented:
Thanks guys and d-glitch. I just want to ask one more thing, is it OK to post book examples with page numbers if I am not be able to understand it or my teacher work if there is something in the steps I need help?

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