Math

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Find the number of elements in A1∪A2∪A3, supposing that there are
103 elements in A1,
992 elements in A2,
10011 elements in A3,
in each of the following situations:

(a) The sets are pairwise disjoint, that is, no pair has common elements, that is, the intersection of the two sets in any given pair is empty.



(b) A1⊆A2⊆A3.



(c) Each pairwise intersection of these sets has the same cardinality 16 , and the intersection of all three sets has cardinality 2.

  • Math -

    a) just add them 11106

    b) They are all in A3 so 10011


    c) draw a Venn diagram
    Only in A1 = 103 - 44 = 59
    Only in A2 = 992- 44= 948
    Only in A3 = 10011 - 44 = 9967
    shared = 3*14 + 2 = 44
    sum = 11018

  • Math C redone -

    should subtract 30 (14*2+2), not 44
    c) draw a Venn diagram
    Only in A1 = 103 - 30 = 73
    Only in A2 = 992- 30= 962
    Only in A3 = 10011 - 30 = 9981
    shared = 3*14 + 2 = 44
    sum = 11060

  • Math -

    Thanks man!

  • Math -

    You are welcome :)

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