Let U = {1, 2, 3, 4, 5} and A = {1, 2, 3}. Find A′.

Verified step by step guidance

1. Identify the universal set U, which is \( U = \{1, 2, 3, 4, 5\} \).
2. Identify the set A, which is \( A = \{1, 2, 3\} \).
3. Understand that A' (A complement) consists of all elements in U that are not in A.
4. List the elements in U that are not in A. These are the elements that will be in A'.
5. Conclude that A' is the set of elements \( \{4, 5\} \).

Key Concepts

Universal Set

The universal set, denoted as U, is the set that contains all possible elements relevant to a particular discussion or problem. In this case, U = {1, 2, 3, 4, 5} includes all elements under consideration, providing a context for defining subsets and their complements.

Subset

A subset is a set whose elements are all contained within another set. Here, A = {1, 2, 3} is a subset of the universal set U. Understanding subsets is crucial for operations involving set theory, such as finding complements.

Complement of a Set

The complement of a set A, denoted as A′, consists of all elements in the universal set U that are not in A. For the given sets, A′ would include the elements {4, 5}, which are in U but not in A. This concept is fundamental in set theory for distinguishing between included and excluded elements.