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Discrete Structures 3.1: Set Theory
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Discrete Structures 3.1: Set Theory

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Questions and Answers

Which symbol is used to indicate that one set is a subset of another set?

  • ⊂ (correct)
  • ∩
  • ∪
  • ∉

    • What does the symbol |S| represent for a finite set S?

  • Intersection of elements in S
  • Number of elements in S (correct)
  • Complement of S
  • Union of elements in S

    • In set theory, what does the power set P(A) represent if A = n?

  • n^2
  • 2 * n
  • 2^n (correct)
  • n!

    • Which type of set is characterized by having the property that no matter how many elements are listed, there are always more elements not on the list?

    <p>Infinite set</p> Signup and view all the answers

    What is the term for sets that don't have elements in common?

    <p>Disjoint sets</p> Signup and view all the answers

    Which of the following best describes a set?

    <p>A collection of objects separated by commas and enclosed in curly brackets</p> Signup and view all the answers

    What is the universal set typically represented by in set theory?

    <p>U</p> Signup and view all the answers

    How is the set {2, 4, 6, 8, 10} commonly represented in set theory?

    <p>{even whole numbers less than 12}</p> Signup and view all the answers

    In a Venn diagram, what does the region inside a circle represent?

    <p>The set being represented</p> Signup and view all the answers

    What does the larger rectangle in a Venn diagram typically represent?

    <p>The universal set</p> Signup and view all the answers

    Which of the following is a correct description of the set S = {odd whole numbers less than 10}?

    <p>S = {1, 3, 5, 7, 9}</p> Signup and view all the answers

    What does the universal set typically represent in set theory?

    <p>The largest set in consideration</p> Signup and view all the answers

    How is the set {0} commonly represented in set theory?

    <p>S = {0}</p> Signup and view all the answers

    What does the power set P(A) represent for a set A with n elements?

    <p>The set of all subsets of A</p> Signup and view all the answers

    What is the term for a set that contains no elements?

    <p>Empty set</p> Signup and view all the answers

    Which symbol is used to indicate that one set is a proper subset of another set?

    <p>$\subset$</p> Signup and view all the answers

    What does the symbol |S| represent for a finite set S?

    <p>The cardinality of the set S</p> Signup and view all the answers

    What type of set is characterized by having the property that no matter how many elements are listed, there are always more elements not on the list?

    <p>Infinite set</p> Signup and view all the answers

    In a Venn diagram, what does the region outside a circle represent?

    <p>$A^c$</p> Signup and view all the answers

    "No matter how many elements are listed, there are always more elements not on the list" characterizes which type of set?

    <p>$\mathbb{N}$</p> Signup and view all the answers

    How can a set be described by writing a description of its elements?

    <p>By writing a description of its elements between curly brackets.</p> Signup and view all the answers

    What is the term for the larger set that contains all the elements in all the sets being considered?

    <p>Universal set</p> Signup and view all the answers

    What is the term for a set that contains no elements?

    <p>Empty set</p> Signup and view all the answers

    What does the symbol |S| represent for a finite set S?

    <p>The number of elements in set S</p> Signup and view all the answers

    What does the power set P(A) represent for a set A with n elements?

    <p>The set of all subsets of A</p> Signup and view all the answers

    What does the region inside a circle represent in a Venn diagram?

    <p>The elements of the set represented by the circle</p> Signup and view all the answers

    What does the region outside a circle represent in a Venn diagram?

    <p>The elements not in the set represented by the circle</p> Signup and view all the answers

    Which symbol is used to indicate that one set is a proper subset of another set?

    <p>⊂</p> Signup and view all the answers

    Which type of set is characterized by the property that no matter how many elements are listed, there are always more elements not on the list?

    <p>Infinite set</p> Signup and view all the answers

    How is the set {2, 4, 6, 8, 10} commonly represented in set theory?

    <p>As a set of even numbers less than or equal to 10</p> Signup and view all the answers

    Study Notes

    Set Theory Notations and Concepts

    • The symbol ⊆ is used to indicate that one set is a subset of another set.
    • The symbol ⊂ is used to indicate that one set is a proper subset of another set.
    • |S| represents the cardinality or the number of elements in a finite set S.
    • The power set P(A) represents the set of all possible subsets of a set A, including the empty set and the set A itself, when A has n elements.

    Set Types and Properties

    • A set that has no elements in common with another set is called disjoint.
    • An infinite set is characterized by the property that no matter how many elements are listed, there are always more elements not on the list.
    • A set that contains no elements is called an empty set or null set.
    • A set can be described by writing a description of its elements, such as {odd whole numbers less than 10}.

    Venn Diagrams

    • The region inside a circle in a Venn diagram represents the elements of a set.
    • The larger rectangle in a Venn diagram typically represents the universal set, which is the set that contains all the elements in all the sets being considered.
    • The region outside a circle in a Venn diagram represents the elements that are not in the set.

    Set Representation

    • A set can be represented by listing its elements, such as {2, 4, 6, 8, 10}.
    • A set can also be represented by writing a description of its elements.
    • The set {0} is commonly represented by ∅ or { }.

    Universal Set

    • The universal set, typically represented by U, is the set that contains all the elements in all the sets being considered.
    • The universal set represents the total set of all possible elements.

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    Description

    Learn about the fundamentals of set theory, including how to describe a set by listing its elements and by writing a description of its elements. Explore the concept of sets and their elements within the realm of discrete structures.

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