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1. If A = 1 B = [1 5 7] Find AB.
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2. Raju, Charu, Shelly are the students of 12th class. Raju has 15 books and 6 pens, Charu has 10
books and 2 pens and Shelly has 13 books and 5 pens. Express this in matrix form.
-1
3. Find P if it exists where P = = 10 --2 .
--5
1
4. Find the cross product of vectors a = i + 2j + k and b = i + 3j + 4k.
5. Find the sum of the vectors a = i – 2j + k and b = –2i + 4j + 5k.
Set Theory
In this module, we will try to explain the fusion of set theory (a branch of mathematics) and relational databases
(RDBMS), which are a part of computer science. We will also learn how the principles of set theory can help to retrieve
data from a database, and this data can then be used for training AI models.
Before we get into the relationship between set and database of sets, we first need to understand few terms.
A Set is an unordered collection of objects, known as elements or members of the set. An element ‘a’ belongs to a set
A. This can be written as ‘a → A’. If a is not an element of set A, then we write ‘a → A’. For examples:
Set of even numbers between 5 and 15: {6,8,10,12,14}.
Set of 5 prime numbers: {2, 3, 5, 7, 11}.
Set of names of grade XI students: {‘Anuj’, ‘Bobby’, ‘Hemant’, ..............}.
We use databases (like Oracle, MS SQL Server, MySQL, etc.) to store digital data. A database is a collection of data.
Database stores the data in the form of tables. For example, the student database has 2 tables as follows:
Student Teacher
Rollno Name T No. TName
101 Vivek T01 Mr. Neeraj
103 Punit T02 Mr. Govind
106 John
The value of data in database tables (also known as relationships) is very small, unless data from different tables are
combined and manipulated to generate useful information. From here begins the role of relational algebra.
Maths for AI 171

