mathlover28
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- Apr 16, 2020
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In the textbook from which this question comes does N contain 0 ? or not?I just come across difficulties when handling this problem.
I know a must be odd and b must be even. But how would I count how many elements in the set A and B, other than listing out all the elements?
In my course, natural number does not contain 0.In the textbook from which this question comes does N contain 0 ? or not?
That makes a difference. It means that set A contains all odd positive integers 3,5,7.⋯4039.In my course, natural number does not contain 0.
There are 2019 elements in set A.That makes a difference. It means that set A contains all odd positive integers 3,5,7.⋯4039.
How many are in set A ?
If you follow the posting guidelines then you must post your work.
153=3375 BUT 163=4096 this limits the size of numbers in (\\mathcal{A}\cap\mathcal{B}\)There are 2019 elements in set A. This is what I literally wrote down for this problem:
Note that A contains odd integers {3,5,7,9,...,4039}. For the set A and B, the elements must also be odd.
i.e. Both a and b+1 are odd. Hence b is even and b >= 2.
Then I am struggling do I really need to count all the elements or not.
EDITED153=3375 BUT 163=4096 this limits the size of numbers in A∩B
Since B={k(2j+1)3: {k,j}⊂N, we can see for example k=1 & 2j+1≤15 would give numbers in both sets.
k=3 & 2j+1≤11 would give numbers in both sets BUT not k=3 & 2j+1=13 would give numbers in both sets.
Can you finish?
I almost arrive the final answer. Thanks a lot!EDITED