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

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Recall that the notation \(D \subseteq A\) means that set \(D\) is a subset of set \(A\), which implies every element of \(D\) must also be an element of \(A\).

List the elements of set \(D\): \(D = \{2, 10\}\).

List the elements of set \(A\): \(A = \{2, 4, 6, 8, 10, 12\}\).

Check each element of \(D\) to see if it is contained in \(A\): verify if \(2 \in A\) and if \(10 \in A\).

If all elements of \(D\) are found in \(A\), then the statement \(D \subseteq A\) is true; otherwise, it is false.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Subset Definition

A set D is a subset of set A if every element of D is also an element of A. This means all members of D must be contained within A for D ⊆ A to be true.

Set Membership

Set membership refers to whether an element belongs to a particular set. To verify subset relations, you must check if each element of one set is present in the other.

Universal Set Context

The universal set U contains all elements under consideration. Understanding U helps clarify the scope of sets A, B, C, and D, ensuring no elements outside U are mistakenly included.

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