Question

Let U be a fixed non-empty set, and let V be the power set of U:

A) V is the set of all subsets of U
B) V is the set of all elements in U
C) V is the set of all prime numbers in U
D) V is the set of all odd numbers in U

Answer 1

The power set V of a set U includes all the possible subsets of U, therefore the correct answer is V is the set of all subsets of U.

Step-by-step explanation:

The power set is a fundamental concept in set theory, a branch of mathematics. Given a set U, the power set of U, denoted as V, includes all the possible subsets of U, including the empty set and U itself. Therefore, the correct answer regarding the power set V is: A) V is the set of all subsets of U. This includes both the null set and U, as well as any other combination of elements that are contained within the original set U.