Questions and Answers
What is the union of two sets?
What symbol represents the union of two sets?
∪
If A = {..., -3, -2, -1} and B = {0, 1, 2, 3,...}, what is A ∪ B?
{..., -3, -2, -1, 0, 1, 2, 3,...}
If P = {1, 2, 3} and Q = {2, 3, 4}, what is P ∪ Q?
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What is the intersection of two sets?
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What symbol represents the intersection of two sets?
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If A = {1, 2, 3} and B = {2, 3, 4}, what is A ∩ B?
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If D ⊆ C, then C ∩ D = D.
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What is the intersection of odd numbers and even numbers?
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Which of the following are operations in the algebra of sets?
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Match the following set operations with their results.
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What is D ∩ (E ∩ F) given D = {whole numbers}, E = {perfect squares between 1 and 9}, F = {even numbers < 9}?
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What is E ∪ F given E = {perfect squares between 1 and 9}, F = {even numbers < 9}?
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What is D ∩ F given D = {whole numbers} and F = {even numbers < 9}?
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What does the expression D ∪ F mean given D = {whole numbers} and F = {even numbers between 10 and 20}?
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The intersection of a set of whole numbers and even numbers between 20 and 30 is not empty.
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Match the following results of set operations given D, E, and F.
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What is the difference between the union and intersection of two sets?
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Study Notes
Union of Sets
- Union combines elements from two sets, including all distinct elements from both.
- Symbol for union is ∪, indicating the inclusion of elements from either set.
- Example: For sets A = {..., -3, -2, -1} and B = {0, 1, 2, 3,...}, A ∪ B yields the set of all integers.
Intersection of Sets
- Intersection includes only elements found in both sets.
- Symbol for intersection is ∩.
- Example: For sets A = {1, 2, 3} and B = {2, 3, 4}, A ∩ B is {2, 3}.
Properties of Sets
- A subset relationship indicates if all elements of one set are contained in another.
- If D is a subset of C, then C ∩ D = D, meaning the intersection will equal the smaller set.
Empty Set
- Intersection of mutually exclusive sets is the empty set.
- Example: Sets E (odd numbers) and F (even numbers) have no elements in common, hence E ∩ F = ∅.
Operations in Set Algebra
- Key operations include union and intersection.
- Other operations may exist but are not defined in this context.
Set Matching Examples
- For sets A = {1, 2, 3, 4, 5}, B = {2, 4, 6}, and C = {1, 3, 5}:
- A ∪ B = {1, 2, 3, 4, 5, 6}
- A ∩ B = {2, 4}
- B ∩ C = ∅
Specific Set Definitions
- D = {x | x is a whole number}
- E = {x | x is a perfect square between 1 and 9}
- F = {x | x is an even number greater than or equal to 2 and less than 9}
Examples of Specific Set Operations
- D ∩ (E ∩ F) reveals elements common to all three defined sets.
- E ∪ F produces the union of perfect squares and specified even numbers.
Additional Set Operations
- Union and intersection produce distinct outcomes:
- D ∪ F includes all whole numbers.
- D ∩ F may include even whole numbers within a specific range.
True Statements about Set Operations
- Calculating intersections and unions provide insights into the relationships among defined sets.
- The empty set can appear as a result of certain intersections.
Construction with Sets
- Operations like A ∪ ∅ result in set A, while intersections with ∅ yield the empty set, demonstrating the identity and property elements of sets.
Conceptual Differences
- Union represents all unique elements from two sets, while intersection focuses on shared elements.
- Union is denoted by A ∪ B; intersection is denoted by A ∩ B.
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Description
Test your knowledge of the operations of sets, focusing on union definitions and examples. This quiz will help reinforce your understanding of how to combine sets and work with their elements effectively.
