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 ⊆ A3.b) the sets are pairwise disjoint.c) there are two elements common to each pair of sets and one element in all three sets.

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 A3a) If A1 ⊆ A2 and A2 ⊆ A3then union will contain the same number of elements as that of A3i.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 setsWe subtract common elements pairwise and add common element in 3i.e. [tex]n(A1 ∪A2 ∪A3) = 100+1000+10000-2-2-2+1\\= 10995[/tex]