Question

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.

Answer 1

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

Answer 2

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

Answer 3

Thanks man!

Answer 4

You are welcome :)