Math
posted by Connor on .
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.

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 
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 
Thanks man!

You are welcome :)