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Len [333]
3 years ago
14

Find the number of elements in A1 ∪A2 ∪A3 if there are 100 elements in A1, 1000 in A2, and 10,000 in A3 if a) A1 ⊆ A2 and A2 ⊆ A

3. b) the sets are pairwise disjoint. c) there are two elements common to each pair of sets and one element in all three sets.
Mathematics
1 answer:
Stella [2.4K]3 years ago
5 0

Answer:

Step-by-step explanation:

Given that there are 3 sets such that  there are 100 elements in A1, 1000 in A2, and 10,000 in A3

a) If A1 ⊆ A2 and A2 ⊆ A3

then union will contain the same number of elements as that of A3

i.e. n(A1 ∪A2 ∪A3)=n(A3) =10000

b) If the sets are pairwise disjoint.

union will contain the sum of elements of each set

n(A1 ∪A2 ∪A3) = 100+1000+10000=11100

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

We subtract common elements pairwise and add common element in 3

i.e. n(A1 ∪A2 ∪A3) = 100+1000+10000-2-2-2+1\\= 10995

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