Discrete Mathematics - Vol 1 | 15. Sets by Abraham | Learn Smarter
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Knowledge
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.

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Sections

  • 15

    Sets

    This section introduces the concept of sets, their definitions, and various operations associated with them.

    Learning Practice

  • 15.1

    Definition Of Sets

    This section introduces the concept of sets as unordered collections of objects, explaining their definitions, notations, types, and fundamental operations.

    Learning Practice

  • 15.2

    Methods Of Expressing A Set

    This section discusses two primary methods for expressing a set: the roster method and the set-builder method.

    Learning Practice

  • 15.3

    Special Sets

    This section introduces various special sets such as the empty set and singleton set, their definitions, and emphasizes their differences.

    Learning Practice

  • 15.4

    Definitions In The Context Of Sets

    This section explores foundational definitions related to sets, including their characteristics, equality, subsets, and the concepts of cardinality and power sets.

    Learning Practice

  • 15.5

    Cardinality Of A Set

    This section focuses on defining the cardinality of a set, exploring its significance in mathematics, and introducing related concepts such as power sets and types of sets.

    Learning Practice

  • 15.6

    Power Set

    The section introduces the concept of power sets, explaining how they consist of all subsets of a set and the significance of cardinality in determining their size.

    Learning Practice

  • 15.7

    Set Operations

    In this section, we explore fundamental operations involving sets, including union, intersection, difference, and Cartesian products, along with their theoretical foundations.

    Learning Practice

  • 15.8

    Set Identities

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

    Learning Practice

  • 15.9

    Proving Set Identities

    This section explores the principles and methods for proving set identities, focusing on key definitions and operations in set theory.

    Learning Practice

References

ch15.pdf

Class Notes

Memorization

What we have learnt

  • A set is defined as an unor...
  • The roster method and set b...
  • The cardinality of a set is...

Final Test

Revision Tests