Page 173 - Artificial Intellegence_v2.0_Class_11
P. 173

Reboot


                                  0
                                  
                         1.  If A =  1  B = [1 5 7] Find AB.
                                  
                                  2  
                                  


                         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
   168   169   170   171   172   173   174   175   176   177   178