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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. [tex]n(A1 ∪A2 ∪A3)=n(A3) =10000[/tex]
b) If the sets are pairwise disjoint.
union will contain the sum of elements of each set
[tex]n(A1 ∪A2 ∪A3) = 100+1000+10000=11100[/tex]
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. [tex]n(A1 ∪A2 ∪A3) = 100+1000+10000-2-2-2+1\\= 10995[/tex]
The union of these three will contain the same number of elements as that of A3 which is 10,000.
What is a set?
A set is a mathematical model for a collection of items; it comprises elements or members, which may be any mathematical object: numbers, symbols, points in space, lines, other geometrical structures, variables, or even other sets.
As it is given that there are 3 sets where the first set A1 has 100 elements, A2 has 1000 elements, and A3 has 10,000 elements.
1. If A1 ⊆ A2 and A2 ⊆ A3 then the union of these three will contain the same number of elements as that of A3. therefore, we can write,
[tex]n(A1\subseteq A2 \subseteq A3)=n(A3)=10000[/tex]
2. If the sets are pairwise disjoint, then the union will contain the sum of elements of each set, therefore,
[tex]n(A1\subseteq A2 \subseteq A3)=100+1000+10000=11100[/tex]
3. If each pair of sets has two elements in common and one element in each of the three sets, we delete common elements pairwise and add common elements in 3. Thus, we can write,
[tex]n(A1\subseteq A2 \subseteq A3)=100+1000+10000-2-2-2+1=10995[/tex]
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