Lecturer:

Muhammad Beyazid Yeldrim Alhaziva, S.Si., M.Mat.

6^th meeting

Logic and Discrete Mathematics (SD2103)

Data Science Department

Faculty of Science

Sumatera Institute Of Technology

INFO TAUTAN SERTA AKSES LENGKAP SEPUTAR MATA KULIAH LOGIKA & MATEMATIKA DISKRIT

Atau Bisa Diakses Melalui Tautan Berikut

https://linktr.ee/LogikadanMatematikaDiskrit

Outline

Logic and Discrete Mathematics

1

2

3

4

5

6

7

8

9

10

11

12

Contracts & Introductions

Logic Math

Methods of Proof

Set Theory

Logic Math Part II

Operations on Sets

Operations on Sets Part II

Recursion Function

Combination

Combination and Mutation

Mid exam

Mathematical Induction of Recursion

13

14

15

16

Relation

Final Exam

Relation Part II

Graph Theory

Students can understand and explain such as:

1. Operations on Sets

1.1 Union of Sets

The union of 2 or more of a set whose members are all members of A or B or both.

For example :

1.2 Intersection of Sets

The intersection of two sets A and B is the set whose members are shared by both set A and set B.

For example :

1.3 Difference of Sets

The difference between set A and set B is a set whose members are only members of A, but not members of set B.

For example :

• {1, 3, 5} – {1, 2, 3} = {5}, tetapi {1, 2, 3} – {1, 3, 5} = {2}

1.4 Complement of Sets

For example :

1.5 Symmetric Difference of Sets

‘Symmetric Difference’ of 2 sets A and set B is a set whose members are either members of set A or members of set B but not members of both sets simultaneously.

For example :

2. Power Sets

The power set of a set A is a set whose elements are all subsets of A, including the empty set and A itself.

Of a set, we can create its subsets. The set of all subset that can be created from a set is called the power set.

3. Cartesian Product

Cartesian product of set A and set B

SUMMARY

1. Set material is very crucial for data science study programs, especially in logic and discrete mathematics courses.
2. Set operations : Union, Intersection, Difference, Complement, Symmetric Difference.
3. The power set of a set A is a set whose elements are all subsets of A, including the empty set and A itself.
4. The Cartesian product in set theory is a relation consisting of all the tuples for each relation element in A combined with all the elements in relation B.

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REFERENCES

• Kenneth H. Rosen, Discrete Mathematics and Application to Computer Science 5th Edition, Mc Graw-Hill, 2003.

• Rinaldi Munir, Diktat kuliah IF2153 Matematika Diskrit (Edisi Keempat), Teknik Informatika ITB, 2003. (juga diterbitkan dalam bentuk buku oleh Penerbit Informatika.

• Richard Johsonbaugh, Discrete Mathematics, Prentice-Hall, 1997.

TASK

• In one class, 25 of them enjoy using Matlab, 35 enjoy using Maple, and 15 enjoy both. The number of students in the class is ?
• The number of positive numbers less than or equal to 100 that are divisible by 6 or 9 is ?
• In the selection of scholarship recipients, each student must pass a math and English test. Out of 180 participants, 103 passed the math test and 142 passed the English test. How many students are declared as scholarship recipients ?

Submit before:

11:59 pm,

6^th December 2024

Must be submitted in pdf form. Format the file name “Assignment 3_Name_NIM” and upload it to our LinkTree assignment section.

For the next meeting, we’re gonna discuss about

“Operations on Sets Part II & Laws of the Set”

Please read the material in our LinkTree

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Class code: y6nmm64

or scan the barcode below:

THANK YOU