15. Sets - Discrete Mathematics - Vol 1
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15. Sets

15. Sets

The chapter provides a comprehensive introduction to sets, including their definitions, representations, and various operations like union, intersection, and difference. It also discusses set identities and the power set concept, along with notable properties such as equality, subsets, and cardinality of sets.

10 sections

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Sections

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  1. 15

    This section introduces the concept of sets, their definitions, and various...

  2. 15.1
    Definition Of Sets

    This section introduces the concept of sets as unordered collections of...

  3. 15.2
    Methods Of Expressing A Set

    This section discusses two primary methods for expressing a set: the roster...

  4. 15.3
    Special Sets

    This section introduces various special sets such as the empty set and...

  5. 15.4
    Definitions In The Context Of Sets

    This section explores foundational definitions related to sets, including...

  6. 15.5
    Cardinality Of A Set

    This section focuses on defining the cardinality of a set, exploring its...

  7. 15.6

    The section introduces the concept of power sets, explaining how they...

  8. 15.7
    Set Operations

    In this section, we explore fundamental operations involving sets, including...

  9. 15.8
    Set Identities

    This section covers the definition and various identities related to set theory.

  10. 15.9
    Proving Set Identities

    This section explores the principles and methods for proving set identities,...

What we have learnt

  • A set is defined as an unordered collection of objects.
  • The roster method and set builder form are two methods to express a set.
  • The cardinality of a set is the count of its elements, distinguishing between finite and infinite sets.

Key Concepts

-- Set
An unordered collection of distinct objects.
-- Union
The union of two sets A and B is the set of elements that are in either A, B, or both.
-- Intersection
The intersection of two sets A and B consists of elements that are in both A and B.
-- Power Set
The power set of a set S is the set of all possible subsets of S, including the empty set and S itself.
-- Cardinality
The number of elements in a set, denoted by |S|.
-- Subset
A set A is a subset of set B if every element of A is also an element of B.
-- Proper Subset
A set A is a proper subset of set B if A is a subset of B and there exists at least one element in B that is not in A.

Additional Learning Materials

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