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 ⊆ C

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Recall that the notation $A \subseteq C$ means that every element of set $A$ is also an element of set $C$.

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

List the elements of set $C$: $\{4, 10, 12\}$.

Check each element of $A$ to see if it is contained in $C$. For example, verify if $2 \in C$, $4 \in C$, $6 \in C$, and so on.

If all elements of $A$ are found in $C$, then $A \subseteq C$ is true; if any element of $A$ is not in $C$, then $A \subseteq C$ 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 A is a subset of set C (denoted A ⊆ C) if every element of A is also an element of C. This means no element in A can be outside of C. Checking subset relations involves comparing elements of both sets.

Set Elements and Membership

Understanding set membership means knowing which elements belong to a set. To verify if A ⊆ C, you must examine each element of A and confirm it is contained in C. This requires careful element-by-element comparison.

Universal Set Context

The universal set U contains all elements under consideration. While U does not directly affect subset checks, it provides the context for all sets involved, ensuring elements are drawn from a common domain.

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