Let A = {2, 4, 6, 8, 10, 12}, B = {2, 4, 8, 10}, C = {4, 10, 12}, D = {2, 10}, andU = {2, 4, 6, 8, 10, 12, 14}. Determine whether each statement is true or false. A ⊆ U
Verified step by step guidance
1
Identify the definition of a subset: A set A is a subset of a set B if every element of A is also an element of B.
List the elements of set A: \{2, 4, 6, 8, 10, 12\}.
List the elements of set U: \{2, 4, 6, 8, 10, 12, 14\}.
Compare each element of set A with the elements of set U to check if all elements of A are present in U.
Conclude whether A is a subset of U based on the comparison.
Recommended similar problem, with video answer:
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1m
Play a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Set Notation
Set notation is a mathematical language used to describe collections of objects, known as elements. In this context, sets A, B, C, D, and U are defined with specific elements. Understanding how to read and interpret set notation is crucial for determining relationships between sets, such as subsets and intersections.
A subset is a set where all elements are contained within another set. The notation A ⊆ U indicates that set A is a subset of set U, meaning every element in A must also be an element of U. Recognizing subsets is essential for evaluating statements about set relationships, such as the one presented in the question.
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 includes all elements from the sets A, B, C, and D, as well as additional elements. Understanding the concept of a universal set helps in determining whether other sets are subsets of it.