Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 weeks ago

math question?

If J={2,4,6,…,2018,2020}, E={3,6,9,…,2016,2019}, and F={5,10,15,…,2015,2020}, how many elements are there in the set J∩(E∪F)?

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  • 4 weeks ago
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    E is the set of multiples of 3 between 1 and 2020.

    F is the set of multiples of 5 between 1 and 2020.

    J is the set of multiples of 2 (even numbers) in that range.

    So basically you are looking for the multiples of 6 or 10 between 1 and 2020.

    1/6 of the numbers are even multiples of 3 (aka multiples of 6).

    ⌊2020/6⌋ = 336

    1/10 of the numbers are even multiples of 5 (aka multiples of 10).

    ⌊2020/10⌋ = 202

    But we can't blindly just add these two numbers because we would be double-counting multiples of both. We need exclude even multiples of 15 (aka multiples of 30) which would have been counted twice.

    1/30 of the numbers are multiples of 30.

    ⌊2020/30⌋ = 67

    So by the inclusion-exclusion principle, we would add the multiples of 6 and 10, then subtract the multiples of 30.

    336 + 202 - 67

    = 538 - 67

    = 471

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  • david
    Lv 7
    4 weeks ago

    J is even numbers

    E is multiples of 3 ... all are not even

      but a sumset of E is mutipes of 6 which are even === F is immaterial

      6, 12, 18 ... 2016

      which is arithmetic .. d= 6  ... a1 = 6

      an = 2016 = 6 + 6(n-1)  <<<  solve for n

       n = 336  <<<  answer

    • atsuo
      Lv 6
      4 weeks agoReport

      For example , 10 is contained in J∩(E∪F) but 10 is not a multiple of 6 .

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