Posted by **Connor** on Sunday, March 30, 2014 at 9:11pm.

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 -
**Damon**, Sunday, March 30, 2014 at 9:37pm
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 -
**Damon**, Sunday, March 30, 2014 at 9:51pm
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 -
**Connor**, Sunday, March 30, 2014 at 10:12pm
Thanks man!

- Math -
**Damon**, Sunday, March 30, 2014 at 10:13pm
You are welcome :)

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