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.

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.

b) If the sets are pairwise disjoint.

union will contain the sum of elements of each set

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.

step-by-step explanation: you take each of the numbers and divide by the amount then you take the range