Podcast
Questions and Answers
What does the union of two sets A and B represent?
What does the union of two sets A and B represent?
- The elements both in A and B
- The elements in A or B or both (correct)
- The elements not in A or B
- The elements only in A
Which of the following is NOT a property of set operations?
Which of the following is NOT a property of set operations?
- Commutative Property
- Reflexive Property (correct)
- Distributive Property
- Associative Property
What is the symmetric difference of sets A and B defined as?
What is the symmetric difference of sets A and B defined as?
- A - B ∩ B - A
- A ∩ B
- A - B + B - A (correct)
- A ∪ B
If A = {1, 2} and B = {2, 3}, what is the intersection A ∩ B?
If A = {1, 2} and B = {2, 3}, what is the intersection A ∩ B?
Which of the following identifies the complement of set A?
Which of the following identifies the complement of set A?
What is the cardinality of the set of all integers Z?
What is the cardinality of the set of all integers Z?
Which of the following statements is true regarding subsets?
Which of the following statements is true regarding subsets?
How many subsets does the set A = {1, 2, 3} have?
How many subsets does the set A = {1, 2, 3} have?
What defines two sets as disjoint?
What defines two sets as disjoint?
In the equality of sets, which of the following must be proved?
In the equality of sets, which of the following must be proved?
Which notation represents that B is a subset of A?
Which notation represents that B is a subset of A?
What does the notation A⊆A imply?
What does the notation A⊆A imply?
If set E contains even integers and set F contains sums of two odd integers, which conclusion can be made about the equality of E and F?
If set E contains even integers and set F contains sums of two odd integers, which conclusion can be made about the equality of E and F?
Which region in a Venn diagram represents the intersection of sets A and B?
Which region in a Venn diagram represents the intersection of sets A and B?
In a Venn diagram with sets A, B, and C, which area represents (A ∪ B) ∩ C?
In a Venn diagram with sets A, B, and C, which area represents (A ∪ B) ∩ C?
What does the region outside both sets A and B in a Venn diagram represent?
What does the region outside both sets A and B in a Venn diagram represent?
In a Venn diagram, how is the complement of set A represented?
In a Venn diagram, how is the complement of set A represented?
If A = {2, 3, 4, 5, 6} and B = {2, 7, 8, 9, 6}, which region in a Venn diagram would represent A - (B ∩ C) if C = {1, 2, 3, 5, 7}?
If A = {2, 3, 4, 5, 6} and B = {2, 7, 8, 9, 6}, which region in a Venn diagram would represent A - (B ∩ C) if C = {1, 2, 3, 5, 7}?
Flashcards
What is the intersection of two sets?
What is the intersection of two sets?
A set of elements that are in both A and B. This is denoted by: A ∩ B.
What is the union of two sets?
What is the union of two sets?
A set of elements that are in A or B. This is denoted by: A ∪ B.
What does it mean if two sets are comparable?
What does it mean if two sets are comparable?
If A ⊆ B or B ⊆ A, then sets A and B are comparable. This means one set is wholly contained within the other.
What is the set difference of A and B?
What is the set difference of A and B?
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What is the symmetric difference of two sets?
What is the symmetric difference of two sets?
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What is the difference of two sets?
What is the difference of two sets?
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What is the complement of a set?
What is the complement of a set?
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What is (A ∩ B) - C?
What is (A ∩ B) - C?
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Cardinality of a Set
Cardinality of a Set
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Equality of Sets
Equality of Sets
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Subset
Subset
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Proper Subset
Proper Subset
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Power Set
Power Set
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Disjoint Sets
Disjoint Sets
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Set of Integers (Z)
Set of Integers (Z)
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Set of Positive Integers (Z+)
Set of Positive Integers (Z+)
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Study Notes
Cardinality of Sets
- The size of a set is called its cardinality.
- A set is finite if its cardinality is an integer.
- A set is infinite otherwise.
Equality of Sets
- Two sets are equal if they have precisely the same elements.
- For sets E and F, E=F if every element of E is also in F and every element of F is also in E.
Subsets
- Set A is a subset of set B (denoted A⊆B) if every element of A is also an element of B.
- Every set is a subset of itself (A⊆A).
- The empty set (∅) is a subset of every set (∅⊆A).
Power Sets
- The power set of a set S (denoted 2S) is the set of all possible subsets of S.
- The number of subsets of a set with n elements is 2n.
Disjoint Sets
- Two sets are disjoint if they have no elements in common.
- If A & B are disjoint, then the intersection of A and B is empty (AnB=∅).
Set Operations: Union and Intersection
- The union of sets A and B (A∪B) is the set of all elements that are in A or B or both.
- The intersection of sets A and B (A∩B) is the set of all elements that are in both A and B.
Set Operations: Comparability
- Two sets, A and B, are comparable if A⊆B or B⊆A.
- This means that one set is a subset of the other.
Set Operations: Venn Diagrams
- Venn diagrams visually represent relationships between sets.
- They show the overlapping regions that represent the various set intersections.
Set Operations: Three Sets
- Set operations and relationships can be extended to three or more sets.
- Venn diagrams for three sets show more complex overlapping regions
- The intersection of all three sets is the region shared by all three sets.
- The union of all three sets includes all elements from any of the sets.
Set Operations: Set Differences
- A - B represents elements in A but not in B.
- The symmetric difference of A and B (AΔB) consists of elements in either A or B, but not both
- De Morgan's Laws apply to set differences and complements (A-(B∪C) = (A-B)∩(A-C), A-(B∩C) = (A-B)∪(A-C)).
Set Operations: Complements
- The complement of a set A, denoted A’, is the set of all elements in the universal set that are not in A.
- A∪A’ = U (the universal set)
- A∩A’=∅ (the empty set)
Set Operations: Counting Integers
- This discusses finding the number of integers in a specific range divisible by a certain number (or numbers).
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