Question

Given an integer array, how can it be divided into two subsets, a and b, such that the intersection of a and b is null, and the union of a and b is equal to the original array?

A) By randomly selecting elements for subsets a and b.
B) By ensuring that the sum of elements in subset a is equal to the sum of elements in subset b.
C) By partitioning the array based on whether the elements are odd or even.
D) By dividing the array into two subsets based on a specific condition, such as whether the elements are greater or less than a given threshold.

Answer 1

To divide an integer array into two subsets with a null intersection, divide the array based on a specific condition such as elements being greater or less than a threshold. This will ensure that each element belongs to only one subset, satisfying the requirements.

Step-by-step explanation:

The question asks how to divide an integer array into two subsets such that their intersection is null and union equals the original array. The correct method is D) By dividing the array into two subsets based on a specific condition, such as whether elements are greater or less than a given threshold. This ensures each element is included in one subset but not in both, fulfilling the condition for a null intersection and a complete union.

For example, let's consider dividing the set S = {1, 2, 3, 4, 5}. We can create subset A with elements less than 3, A = {1, 2}, and subset B with elements greater than or equal to 3, B = {3, 4, 5}. The intersection of A and B, A ∩ B, is null, and their union, A ∪ B, equals the original set S.

In mathematical terms, we're creating two complementary sets based on a special condition (in this case, a threshold value), which is a fundamental concept in set theory.