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What is the intersection of two sets A and B?
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The intersection of A and B is a set containing only the elements that are present in both A and B, denoted as A ∩ B.
How do equivalent sets differ from equal sets?
Equivalent sets have the same number of elements; equal sets have the same elements.
State the Commutative Law for sets.
A ∪ B = B ∪ A and A ∩ B = B ∩ A.
How do you find the cardinal number of a set?
The cardinal number of a set is the total number of elements in the set.
What is a complement of a set A?
The complement of a set A, denoted A', is the set of all elements not in A.
Explain the distributive law for sets.
The distributive law states that A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C).
What is De Morgan's Law with respect to sets?
De Morgan's Law states that the complement of the union is the intersection of the complements and vice versa: (A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'.
What is the Principle of Inclusion and Exclusion used for?
The Principle of Inclusion and Exclusion is used to calculate the number of elements in the union of multiple sets by including the sizes of the individual sets and subtracting the sizes of their intersections.
What is a power set?
A power set is the set of all subsets of a set, including the empty set and the set itself.
What is the importance of the empty set in set theory?
The empty set is a subset of every set and is crucial in defining set operations and properties.
Define a singleton set.
A singleton set is a set containing exactly one element.
Define the union of two sets A and B.
The union of A and B is a set containing all elements from both A and B, denoted as A ∪ B.
What does the symbol '⊆' represent?
The symbol '⊆' represents 'is a subset of'.
What does the symbol '⊇' represent?
The symbol '⊇' represents 'is a superset of'.
What is a well-defined collection of objects in set theory called?
A set.
What distinguishes a finite set from an infinite set?
A finite set has a specific number of elements, while an infinite set has an unbounded number of elements.
What is the result of the difference of sets A and B (A - B)?
The difference A - B is a set containing all elements of A that are not in B.
What is an empty set?
An empty set is a set that contains no elements, also represented as {} or φ.
How is a set represented in roster form?
In roster form, a set is represented by listing its elements between curly braces, e.g., {1, 2, 3}.
Describe the Cartesian product of two sets A and B.
The Cartesian product A * B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B.
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