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 (C)</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} (D)</p> Signup and view all the answers

How is the intersection of two sets defined?

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

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

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

What defines the Cartesian product of sets A and B?

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

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

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

What is the range of a function defined as?

<p>Set of image elements (C)</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 (C)</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 (D)</p> Signup and view all the answers

What is a bijective function known as?

<p>One-to-one and onto (A)</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 (B)</p> Signup and view all the answers

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