Disjoint Sets, Complement, Cartesian Products
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Questions and Answers

What do sets in mathematics contain?

  • Alphabets and symbols
  • Numbers and letters
  • Equations and formulas
  • Elements or members (correct)

    • How are sets usually denoted?

  • With capital letters (correct)
  • With numbers
  • With small letters
  • With special characters

    • Which notation indicates that set A is a subset of set B?

  • A ≠ B
  • A = B
  • A ⊇ B
  • A ⊆ B (correct)

    • What does an empty set in mathematics signify?

    <p>A set with no elements</p> Signup and view all the answers

    How is the union of two sets expressed in set notation?

    <p>{x: x ∈ A or x ∈ B}</p> Signup and view all the answers

    How is the intersection of two sets defined?

    <p>{x: x ∈ A and x ∈ B}</p> Signup and view all the answers

    Which term is used to define sets A and B that do not share any common elements?

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

    What is the complement of set A, denoted by A'?

    <p>{x: x ∈ U and x ∉ A}</p> Signup and view all the answers

    The difference of sets A and B, denoted as A\B, is equal to:

    <p>{x: x ∈ A and x ∉ B}</p> Signup and view all the answers

    What defines the Cartesian product of sets A and B?

    <p>A set of ordered pairs</p> Signup and view all the answers

    What is a function defined as in terms of Cartesian products?

    <p>A subset of Cartesian products</p> Signup and view all the answers

    What is the range of a function defined as?

    <p>Set of image elements</p> Signup and view all the answers

    What does it mean for a function to be injective?

    <p>Maps distinct elements of A to distinct elements of B</p> Signup and view all the answers

    What is a surjective function characterized by?

    <p>Every element in the codomain has a pre-image in the domain</p> Signup and view all the answers

    What is a bijective function known as?

    <p>One-to-one and onto</p> Signup and view all the answers

    What is the ultimate goal of machine learning and deep learning in terms of functions?

    <p>Learning a function from data</p> Signup and view all the answers

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