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Monday, November 25, 2019

Relation and Functions

Equivalence and partial order relations with examples

 

Equivalence relations:

A relation ‘R’ on set ‘A’ is said to be equivalent if R is 

 

  1. Reflexive. It needs to be diagonal pair such as (a,a),(1,1),(8,8) 
  2. Symmetric: it should have element  such as (a,b) and (b,a) for example (1,4) and (4,1) in the relation set for symmetric
  3. Transitive: It needs to be in the form of (a,b), (b,c) so that we have (a,c)

 

Let us understand with an example

 

A={1,2,3}  elements =2^3 

A(1,1)

A(1,2)

A(1,3)

A(2,1)

A(2,2)

A(2,3)

A(3,1)

A(3,2)

A(3,3)



R1={NULL} it is not reflexive and therefore equivalence does not holds.

R2={(1,1),(2,2) (3,3)} it is reflexive as it has diagonal pairs such as (a,a)

It is symmetric as all diagonal pair makes the set symmetric

Also if also transitive if it has only diagonal elements. 

Therefore the relation is equivalence

R3={(1,1),(2,2) (3,3)(2,1)} It is reflexive as it has all diagonal elements

It is not symmetric as there exist only (2,1) and not (1,2) in R3. There the relation is not in 

equivalence

 

R4={(1,1),(1,3),(2,1)(3,1)} It does not has all diagonal elements ref to table above, hence it does not have equivalence relation

R5={(1,1),(2,2),(3,3),(1,2)(1,3)(2,1)(3,1)} It is reflexive as it has all diagonal elements ref table

It is symmetric as we have (1,2) and (2,1). Also we have (1,3) and (3,1)

 

It is transitive as if we take (1,1) (3,3) then we have (3,1) as in (a,b) and (b,c) we have (a,c) for it to become transitive. Hence equivalence hold here.

R6={(1,1),(1,2),(2,1),(2,3),(3,1)(3,2),(3,3)} It is not reflexive as we do not have all diagonal elements ref table above and you will find (2,2) is missing.



Partial order relations

  1. Reflexive. It needs to be diagonal pair such as (a,a),(1,1),(8,8) 
  2. Anti Symmetric: it should not have element  such as (a,b) and (b,a) for example (1,4) and (4,1) in the relation set for symmetricity. If it has (a,b) and not (b,a) then it is said to be in anti symmetric form
  3. Transitive: It needs to be in the form of (a,b), (b,c) so that we have (a,c)




A=(1,2,3}

 

R1={NULL} it is not reflexive and therefore partial order relation  does not holds.

R2={(1,1),(2,2) (3,3)} it is reflexive as it has diagonal pairs such as (a,a)

It is antii-symmetric. Also it is  transitive if it has only diagonal elements. 

Therefore the relation is in partial order

R3={(1,1),(2,2) (3,3)(2,1)} It is reflexive as it has all diagonal elements

It is anti symmetric as there exist only (2,1) and not (1,2) in R3. There the relation is in 

Partial order

 

R4={(1,1),(1,3),(2,1)(3,1)} It does not has all diagonal elements ref to table above, hence it does not have reflexive property and therefore partial order does not holds for this relation

R5={(1,1),(2,2),(3,3),(1,2)(1,3)(2,1)(3,1)} It is reflexive as it has all diagonal elements ref table

It is symmetric as we have (1,2) and (2,1). Also we have (1,3) and (3,1). Therefore it is not anti symmetric

 

It is transitive as if we take (1,1) (3,3) then we have (3,1) as in (a,b) and (b,c) we have (a,c) for it to become transitive. Hence the relation is not in partial order 

R6={(1,1),(1,2),(2,1),(2,3),(3,1)(3,2),(3,3)} It is not reflexive as we do not have all diagonal elements ref table above and you will find (2,2) is missing.Therefore relation is not set to be in partial order.

 

Sunday, November 3, 2019

Quiz for score improvement

Pick relevant quiz as per your grade
Note: Sign up/Sign in  is not necessary to run the quiz, you can opt for skip for now. Also choose solo practice option. Happy quizzing :)

1) Congruent triangles( Grade 7)
https://quizizz.com/admin/quiz/58308ebe37a4ff9236d1ca82

2) Comparing quantities
https://quizizz.com/admin/quiz/578c78fc1586ece673f76dcc

3) Matrices(University Grade)
https://quizizz.com/admin/quiz/59c95573a1a3171000119052

4) Sets(K12, University)
https://quizizz.com/admin/quiz/5cc13d00ab784b001b1c1511




Thursday, October 10, 2019

BCA DBMS practice

BCA

DBMS Practice terms and concepts 

1. Define Data .
2. Define Information .
3. Differentiate between data and information .
4. Explain the term Field .
5. Explain the term Record .
6. Explain the term file .
7. What is a database ?
8. Explain the term DBMS .
9. What are the components of database system ?
10. Enumerate the major responsibilities of data Administrator ?
11. Differentiate between data Administrator and Database Administrator .
12. What is schema ?
13. What is instance ?
14. What is mapping ?
15. Discuss two advantages of Physical Data Independence .
16. Define data model .
17. list two major advantages of conceptual modeling .
18. Explain the term Entity .
19. What is entity set ?
20. Write the uses of entity sets .
21. What is a relationship type ?
22. Write the uses of E-R model .
23. What is abstraction ?
24. Explain uses of abstaction .
25. Explain data integration .
26. List two major advantages of network Data model .
27. Define the term Relation .
28. Explain uses of foreiegn key .
29. What is domain ?
30. Diffentiate between relation algebra and relational calculas .
31. What is function dependency ?
32. Explain BCNF with an explain .
33. Describe 4NF with an example .

34. What is view ?
OR
Explain views in SQL.

35. Differentiate between DDL and DML.
36. Define query processing .
37. Define Query optimization .
38. What is concurrency ?
39. What is database ? What are the objectives of database ? Also discuss the advantages and disadvantages of database .
40. What is data base system ? Discuss the main objectives of any database system also .

41. What is file processing system ? What are the disadvantages of a file processing system over database system ?
OR
What do you mean by traditional file based system ? What are the limitations of the file processing system / file approach ?

42. What is DBMS ? outline all the functions performed by a DBMS .
OR
Explain DBMS functions with suitable examples .

43. What are the main / common facilities that every DBMS should provide ? Explain .
44. What do you mean by DBMS ? Explain the advantages and disadvantages of DBMS ?

45. Explain the role of DBA .
OR
Explain database administrator briefly with suitable examples .
OR
Discuss duties of database administrator with examples .
OR
What do you mean by database administration (DBA) ? Explain the responsibilities of DBA ?
OR
What are the responsibilities / function of Database administrator (DBA) ?

46. what do you mean by database language ? explain .
OR
Explain DBMS languages briefly with suitable examples .

47. What do you understand by a Query language ? Distinguish between DDL , DML and DCL . Explain any two DDL & DML commands using suitable examples .

48. Explain components of DBMS .

49. Explain the three- level architecture of DBMS with the help of an example .
OR
discuss architecture of DBMS with an example .
OR
What do you mean by Database system architecture ? Explain in detail .
OR
Describe the architecture of a database system .Why a database is described to be an integrated one ?

50. what is data independence and why is it important ?
OR
Describe Data independence with examples .
OR
What do you mean by Data independence ? also explain logical and physical data independence .

51. what is the difference between physical and logical data independence ?

52. Explain client server architecture to DBMS .
OR
Explain client server architecture .

53. What is centralized DBMS ? How is it useful and used ? Explain its disadvantages with examples .
54. Define the term data model . Explain different types of data model with examples .

55. Describe object-based data model with examples .

56. What is ER diagram ? Draw the ER diagram of library management system .

57. What is ER diagram ? Draw the ER diagram of school management system .

58. Define the term E-R diagram . Explain the various types of relationships in a E-R diagram . Draw an E-R diagram . Draw an E-R diagram for taking your own example .
59. Write note on Data abstraction and data Integrity / Integration .
60. Define the term 'data model ' . Explain Hierarchical model in detail .
61. Differentiate between network model and Hierarchical model .
62. Discuss database relations and their properties with examples .

63. What do you mean by key ? Explain different types of key with suitable example .
OR
Example various types of keys with suitable examples .
OR
What do you mean by key ? Explain in detail the different types of keys .

64. Explain integrity constraints . Describe their importance .
65. What are the various operators in relational algebra ? Explain with examples .

66. Define normalization . How is it useful and used ? Explain by giving Examples, the conditions that are necessary for a relation to be in 1NF , 2NF , 3NF , BCNF .
OR
Define normalization . Explain by giving examples , the conditions that are necessary for a relation to be in 1NF , 2NF , 3NF , BCNF , 4NF .
OR
What is normalization ? How is it used and useful ? {you may go up to 3NF} .
OR
What is normalization ? Explain the different types of normalization with suitable example .

67. Write short note on various types of functional dependencies with Examples .

68. "No Loss decomposition is an aid to relational data base design " . Is it true ? If yes them justify it through an appropriate examples .
69. What is SQL? Example its use , purpose and importance through appropriate examples .
70. What is Query processing ? How is it used and useful ? Discuss its Strategies with Examples .
71. Explain Query optimization briefly with examples .

72. what is database security ? Why is it important ? Also discuss the various security ? Why is it important ? also Discuss the various security issues .
OR
Explain database security briefly with examples .

73. What is concurrency control ? how is it implemented ? Explain .
74. Explain database recovery briefly with examples .

Thursday, September 19, 2019

BCA Mathematics Part II

BCA Maths 
Practice Questions-Part II
Matrices and Determinants



Q1    Find the value of a and b




Q2 Find the value of x such that

     
    



Wednesday, September 18, 2019

BCA Mathematics Part I





BCA Mathematics
Practice Question


Q1 Indefinite Integral






Q 2 Definite Integrals




Q3 Differentiation










Q4 Limits and Continuity





continuous at x=1, Find the value of a and b.

Q6 Prove the following
a) Prove function is continuous at x=0


b) Find all points of discontinuity of f, where f is defined by