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Lecture notes Discrete Structures Discrete Mathematics R79,65
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Lecture notes Discrete Structures Discrete Mathematics
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  • Course
  • Discrete Structures
  • Institution
  • Kutaisi International University
  • Book
  • Discrete Mathematics

In this document you will get across various basic and advanced topics of dicrete math.This notes provide straight forward explanation of confusing topics,explainations are by me student of KIU and I try to explain hard problems and theorems in simpler way(using my Brain:) and also Blackbox AI).The...

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  • November 3, 2024
  • 4
  • 2024/2025
  • Class notes
  • Markus neuhauser
  • Class 1 to 5

Subjects

  • dsicrete math
  • university
  • computer science
  • notes
  • straight forward explanation

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DS-notes
Lado Sitchinava

&1 Sets
1.if all element is set 𝐴 and set 𝐵 are equal then we write 𝐴 = 𝐵
2.Intersection of sets are set of all the simlar elements set 𝐴 and set 𝐵 have. we write it as 𝐴 ∩ 𝐵
3.Difference of Set 𝐴 and Set 𝐵 is set of all elements that are in 𝐴 but cannot be found in set 𝐵.
formal definition 𝐴 \ 𝐵
4.Cartesian product of Set 𝐴 and set 𝐵 is set of A’s and B’s elements concatenated. For example:
𝐴 = {1, 2}, 𝐵 = {3, 4}

𝐴𝑋𝐵 = {(1, 3), (1, 4), (2, 3), (2, 4)}

5.power set of set 𝐴 for example is set of all subsets of 𝐴. number of subsetst of 𝐴 is 2𝑛 .n is number
of elements in set 𝐴.

&2 Mathematical induction
I will skip this because its hell easy

&3 Comutativity,associativity and Distributivity
1.Comutativity: 𝐴 ∩ 𝐵 = 𝐵 ∩ 𝐴, 𝐴 ∪ 𝐵 = 𝐵 ∪ 𝐴
2.Associativity: (𝐴 ∪ 𝐵) ∪ 𝐶 = 𝐴 ∪ (𝐵 ∪ 𝐶), (𝐴 ∩ 𝐵) ∩ 𝐶 = 𝐴 ∩ (𝐵 ∩ 𝐶).
3.Distributivity:𝐴 ∪ (𝐵 ∩ 𝐶) = (𝐴 ∪ 𝐵) ∩ (𝐴 ∪ 𝐶),𝐴 ∩ (𝑏 ∪ 𝐶) = (𝐴 ∩ 𝐵) ∪ (𝐴 ∩ 𝐶).
De Morgans’s Laws : 𝐶 \ (𝐴 ∩ 𝐵) = (𝐶 \ 𝐴) ∪ (𝐶 \ 𝐵).

&4 Function and mapping
1.𝑓 : 𝑋 → 𝑌 , here X is domain(განსსაზღვრის არე),Y is co-domain(მნიშვნელობათა არე)
2.Identity function: Let X be a set
𝑋→𝑋
id𝑥 : {𝑥→𝑥 this is called identity function on X

2.Let X and Y be sets.

𝑋×𝑌 →𝑋
𝜋1 : {
(𝑥, 𝑦) → 𝑥

this is called projection on first factor, which means that every (x,y) paris provides output of x.
3.[𝑥] is largest integer smaller or equal to x(მთელი ნაწილი)
4.{x} is smallest integer larger or equal to x(წილადი ნაწილი)

&5 Injectivity,surjectivity, bijectivity
1.definition of injectivity: function’s output is unique in every case for example: one domain should
relate to one co-domain but other domain can not be connected to same co-doamin as first domain

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