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. {0, 2} ⊆ D
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Identify the elements of set D. D = {2, 10}.
Examine the elements of the set {0, 2}.
Check if every element of {0, 2} is also an element of set D.
Notice that the element 0 is not in set D.
Conclude whether {0, 2} is a subset of D based on the presence of all its elements in D.
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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 are represented by curly braces, and elements are listed within them. 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 its elements are also contained within another set. The notation 'A ⊆ B' indicates that set A is a subset of set B. To determine if a set is a subset, one must check if every element of the first set exists in the second set, which is essential for evaluating statements about set relationships.
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. Understanding the universal set helps in contextualizing other sets and determining the validity of subset relationships within the defined universe.