Find the number of elements in A 1 ∪ A 2 ∪ A 3 if there are 200 elements in A 1 , 1000 in A 2 , and 5, 000 in A 3 if (a) A 1 ⊆ A
2 and A 2 ⊆ A 3 . (b) the sets are pairwise disjoint. (c) There are two elements in common to each pair of sets and one element in all three sets.
1 answer:
Answer:
a. 4600
b. 6200
c. 6193
Step-by-step explanation:
Let
the number of elements in A.
Remember, the number of elements in
satisfies

Then,
a) If
, and if 
Since 
So

b) Since the sets are pairwise disjoint

c) Since there are two elements in common to each pair of sets and one element in all three sets, then

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