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Math Help - sets

  1. #1
    Senior Member sfspitfire23's Avatar
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    sets

    Given two sets A: {15, 16, 17, 18, 19} and B: {8, 9, 10, 11, 12, 13, 14}. If C= A + B, then how many distinct values are possible for C?

    12?
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  2. #2
    Super Member Bacterius's Avatar
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    Well notice that the set A + B is neither included in the set A nor in the set B. Therefore the number of combinations are 5 (the number of elements in A) + 7 (the number of elements in B) = 12.

    That is because the smallest element in A is 15, and in B it is 8. Yet, 15 + 8 = 23 which is greater than the greatest element in A or B. Do it the other way too, and you have a proof (I think ).
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  3. #3
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by sfspitfire23 View Post
    Given two sets A: {15, 16, 17, 18, 19} and B: {8, 9, 10, 11, 12, 13, 14}. If C= A + B, then how many distinct values are possible for C?

    12?
    I think you mean c = a + b, where a in A and b in B.

    Minimum is 15+8=23, max is 19+14=33, which makes 11 possibilities.
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