Question

Find the union and the intersection of the following family:

B=Bₙ:n∈N

where Bₙ =N∪0−1,2,3,…,n.

A. Union: N−0,1, Intersection: ∅

B. Union: N−0, Intersection: ∅

C. Union: N−0, Intersection: 0

D. Union: N−1, Intersection: ∅

Answer 1

The union of the family of sets B is the set of all natural numbers except for 1, and the intersection is the set containing only the number zero.

Step-by-step explanation:

To find the union and intersection of the family of sets B, first we should understand what each set Bn in the family looks like. Each set Bn includes all natural numbers (N) and the number 0, but it excludes the first n positive integers. Essentially, Bn = {0, n+1, n+2, n+3, ...}.

The union of all sets Bn as n ranges over all natural numbers would be the set of all natural numbers except for 1, since for any other natural number there is a set Bn that does not exclude it. Therefore, the union is N - {1}.

The intersection of all sets Bn would be the set of all elements that are in every Bn. Since each Bn excludes the first n positive integers, there are no positive integers that are in every set. However, 0 is included in every set Bn, so the intersection is {0}.