List the elements in each set. See Example 1. {p|p is a number whose absolute value is 4}
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- 0. Review of College Algebra4h 45m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
0. Review of College Algebra
Functions
Problem 27
Textbook Question
Concept Check Let A = {1, 2, 3, 4, 5, 6}, B = {1, 3, 5,}, C = {1, 6}, and D = {4}. Find each set. a. A ∩ D b. B ∩ C c. B ∩ A d. C ∩ A
Verified step by step guidance1
Recall that the intersection of two sets, denoted by \(A \cap B\), is the set of all elements that are common to both sets \(A\) and \(B\).
For part (a), find \(A \cap D\) by identifying elements that are in both \(A = \{1, 2, 3, 4, 5, 6\}\) and \(D = \{4\}\).
For part (b), find \(B \cap C\) by identifying elements common to \(B = \{1, 3, 5\}\) and \(C = \{1, 6\}\).
For part (c), find \(B \cap A\) by identifying elements common to \(B = \{1, 3, 5\}\) and \(A = \{1, 2, 3, 4, 5, 6\}\). Note that since \(B\) is a subset of \(A\), this intersection will be \(B\) itself.
For part (d), find \(C \cap A\) by identifying elements common to \(C = \{1, 6\}\) and \(A = \{1, 2, 3, 4, 5, 6\}\). Since \(C\) is a subset of \(A\), this intersection will be \(C\) itself.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Set Intersection
The intersection of two sets includes all elements that are common to both sets. It is denoted by the symbol '∩'. For example, if Set A = {1, 2, 3} and Set B = {2, 3, 4}, then A ∩ B = {2, 3}.
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Set Notation and Elements
Sets are collections of distinct elements, usually enclosed in curly braces {}. Understanding how to read and interpret these elements is essential for performing operations like union, intersection, and difference.
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Basic Set Operations
Besides intersection, basic set operations include union (combining elements from both sets) and difference (elements in one set but not the other). Knowing these helps in manipulating and understanding relationships between sets.
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