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Disjoint Sets, Complement, Cartesian Products

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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?

A set with no elements Signup and view all the answers

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

{x: x ∈ A or x ∈ B} Signup and view all the answers

How is the intersection of two sets defined?

{x: x ∈ A and x ∈ B} Signup and view all the answers

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

Disjoint sets Signup and view all the answers

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

{x: x ∈ U and x ∉ A} Signup and view all the answers

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

{x: x ∈ A and x ∉ B} Signup and view all the answers

What defines the Cartesian product of sets A and B?

A set of ordered pairs Signup and view all the answers

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

A subset of Cartesian products Signup and view all the answers

What is the range of a function defined as?

Set of image elements Signup and view all the answers

What does it mean for a function to be injective?

Maps distinct elements of A to distinct elements of B Signup and view all the answers

What is a surjective function characterized by?

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

What is a bijective function known as?

One-to-one and onto Signup and view all the answers

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

Learning a function from data Signup and view all the answers