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. D ⊆ A

Verified step by step guidance

1. Identify the elements of set D, which are {2, 10}.
2. Identify the elements of set A, which are {2, 4, 6, 8, 10, 12}.
3. Check if every element of set D is also an element of set A.
4. Since both elements of D (2 and 10) are found in A, set D is a subset of set A.
5. Conclude whether the statement 'D ⊆ A' is true or false based on the subset relationship established in the previous steps.

Key Concepts

Set Notation

Set notation is a mathematical language used to describe collections of objects, known as elements. In this context, sets are denoted by curly braces, and elements are separated by commas. Understanding how to read and interpret set notation is crucial for determining relationships between sets, such as subsets and intersections.

Subset

A subset is a set where all its elements are also contained within another set. The notation 'D ⊆ A' indicates that set D is a subset of set A, meaning every element in D must also be an element of A. Recognizing subsets is essential for evaluating statements about set relationships.

Element Membership

Element membership refers to whether a specific item is included in a set. The symbol '∈' denotes that an element belongs to a set, while '∉' indicates it does not. To determine if 'D ⊆ A' is true, one must check if each element of D is present in A, which requires a clear understanding of element membership.