Question

Find the number of elements in A1 ∪ A2 ∪ A3 if there are 96 elements in A₁, 1004 elements in A₂ and 10050 elements in A₃ in each of the following situations:

(a) The sets are pairwise disjoint.

Answer 1

When the sets A1, A2, and A3 are pairwise disjoint, the number of elements in the union A1 ∪ A2 ∪ A3 is the sum of the elements in each set, which equals 11150.

Step-by-step explanation:

To find the number of elements in the union of sets A1 ∪ A2 ∪ A3, we must consider the given information about the sets. In situation (a), where the sets are pairwise disjoint, we simply sum the number of elements in each set.

The number of elements in A1 is 96, in A2 is 1004, and in A3 is 10050. Since there is no overlap among the sets (pairwise disjoint), the total number of elements in the union is the sum of the numbers of elements in each set:

Number of elements in A1 ∪ A2 ∪ A3 = Number of elements in A1 + Number of elements in A2 + Number of elements in A3

Number of elements in A1 ∪ A2 ∪ A3 = 96 + 1004 + 10050

= 11150