Textbook Question
In Exercises 59–70, evaluate each exponential expression. (-10)^2
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0. Review of Algebra
Exponents
1:21 minutesProblem 62
Textbook Question
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
Verified step by step guidance1
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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Video duration:
1mKey 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.
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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.
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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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