Messages

1

Basic Maths / Re: Co-Ordinate Geometry

« on: April 05, 2016, 04:33:32 PM »

Formula

1.   Distance between two points,       d = √(x2-x1)2 + (y2-y1)2

2.   Coordinates of a mid-points, (xm , Ym),     xm  = (x1+x2)/2  ,      Ym  = (y1+y2)/2                         

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Basic Maths / Re: Theory of sets

« on: April 05, 2016, 04:32:42 PM »

SETS OF SETS
The objects of a set can be the sets themselves. In that case we are talking about a family of sets or a class of sets, which is denoted by capital letters A, B, C, … In the same time, the capital letters denote their elements.
UNIVERSAL SET
Sometimes we are interested only in the subsets of one set, and other sets have no meaning for our consideration. In such a case we call this set the universal set. The set of all points in one plane can be the universal set.
John is at a party. All the girls at the party are a universal set for John, because he is interested whether they will like him.
POWER SET
The power set is the family of all subsets of a set. If A is a set, then its power set is denoted by 2A or P(A).
For example, if A = {1,2}, then 2A = { {1,2}, {1}, {2},  }.

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Basic Maths / Re: Theory of sets

« on: April 05, 2016, 04:32:19 PM »

SUBSET
Let A be the set of all Blondies and let B be the set of all women. All the blondies are women, but all women are not blondies. The set of blondies is a subset of the set of women. If all the women were Blondies then the set of Blondies would be equal to the set of women.
A is a subset of  B if every element in set A is also a member of set B. A is a subset of B if a  A implies a  B. We denote that by A  B which is also read 'A is contained in B'.
Definition: Two sets A and B are equal (A = B), if and only if A  B and B  A.
Notification B  A means 'B is superset of A' or 'B contains A'. If A is not a subset of B, we write A  B. That means that there is at least one element in A that is not a member of B.
The null set is a subset of every set.
If A  B and A  B then we call A the proper subset of B and denote it by A  B.
Every set is a subset of itself.
Definition: A is a proper subset of B if:
A is a subset of B
A is not equal to B
i.e. A   B and A  B
Two sets are comparable if one of the sets is a subset of the other set, i.e. A  B or B  A.
Every set is equal to itself, i.e. (A = B)  (B = A) and A = B and B = C implies A = C.
 Theorem: If A is a subset of B and B is a subset of C, then A is a subset of C.
A  B and B  C  A  C
Proof: Let x  A. Since A  B  x  B. By the consideration B  C, every element of B, which includes x, is a member of C. We know that x  A  x  C according to the definition A  C.

4

Basic Maths / Re: Theory of sets

« on: April 02, 2016, 01:07:19 PM »

EQUALITY OF SETS
All girls in the class like John. All girls in the class like to eat pizza. The set of girls who like John is equal to the set of girls who like pizza.
Let A and B be sets. Consider that every element of set A is also an element of set B. Set A is equal to the set B if they both have the same members. The equality of sets A and B is denoted by A = B and with (  a  A)( a  A  a  B). This means that each element of the set A is also element of the set B. Here the symbol  means ‘each’. The symbol  means that if a   A, then a  B. We read it "a   A implies a   B" or " from a    A outcomes a  B".
Example: The set {a, b, c, d} is equal to the set {c, a, d, b}, i.e.
{a, b, c, d} = {c, a, d, b}. 
The set {a, b, c} is different from the set {a, b}, i.e.
{a, b, c}  {a, b}.
Let N be the set of all natural numbers. If S = {x | x  N, x < 4} and A = {1, 2, 3},
Then S = A.
NULL SET
Let S be the set of Blondies who are clever. The set S is empty. (Remark: This is just a joke, as we know that IQ does not depend on the colour of the hair.)
Let N be the set of all natural numbers. Then the set {x | x  N,   x2 = 6} is an empty set because there is no natural number whose square is 6.
An empty set is a set with no elements. We denote it by the symbol  and call it the null set. 

5

Basic Maths / Re: Co-Ordinate Geometry

« on: March 31, 2016, 11:46:27 AM »

Parallelograms
________________________________________
Definition of a Parallelogram
A parallelogram is a quadrilateral that has two pairs of parallel sides.

Any two opposite sides of a parallelogram are called bases, a distance between them is called a height.

   

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Basic Maths / Re: Co-Ordinate Geometry

« on: March 31, 2016, 11:46:03 AM »

Trapezoid

A quadrangle which has only one of the two opposite sides as parallel is called a Trapezoid.

The other opposite sides need not be parallel. If both pair of opposite sides of a trapezoid are parallel then it becomes a parallelogram. The trapezoid does not follow the basic properties of a parallelogram.

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Basic Maths / Co-Ordinate Geometry

« on: March 31, 2016, 11:45:47 AM »

Some Important Definition of Geometry

Difference between a rectangle and a square:
1.  Only opposite sides of a rectangle are equal unlike square which has all sides equal.

Difference between a rectangle and a rhombus:

1.  Each angle of rectangle is 90 degrees unlike rhombus where angles are not equal to 90 degrees.

Difference between a Parallelogram and a rhombus:
If all sides of parallelogram are equal but angles are not equal to 90 degrees, then this parallelogram is called a rhombus.

Difference between a Rhombus and a square (Rhombus and square have all sides equal) : 

1.  Each angle of square has to be 90 degrees unlike rhombus.

Difference between a rectangle & a Rhombus:
1. Each angle of rectangle has to be 90 degrees unlike rhombus.

2. Unlike rhombus only opposite sides of rectangle are equal.

A square is a parallelogram with right angles and equal sides. A square is a particular case of a rectangle and a rhombus simultaneously. So, it shows both the properties of rhombus and rectangle simultaneously.

Square can be differentiated from a rectangle and rhombus due to following properties.
1. Unlike rectangle square needs to have all its sides equal.

2. Unlike rhombus square needs to have all angles equal to 90 degree.

Difference between the circumcenter and a centroid of a triangle.
The circumcenter is a point that is equidistant from all three vertices so that a circle can be drawn that passes through three vertices. The circle circumscribes the triangle and the triangle is inscribed in the circle.

The centroid is the center of gravity of the triangle. It is the point where the three altitudes of the triangle intersect. If it is an acute triangle, the intersection will take place inside the triangle. If you cut a triangle from a piece of cardboard, the triangle would balance perfectly on the head of a pin place at the centroid.

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Basic Maths / Re: Theory of sets

« on: March 31, 2016, 11:44:40 AM »

Listing an element twice in a set does not add to its membership. The order in which elements are listed does not matter either.
In mathematics there are a lot of statements and definitions that are considered to be true without proof, but there are a lot of statements and theorems that are proved by the use of previous assumptions and definitions.

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Basic Maths / Re: Theory of sets

« on: March 31, 2016, 11:44:08 AM »

We denote sets with uppercase letters, for example: A, B, C, S, X, Y,…
The elements of sets are denoted by lowercase letters: a, b, c, x, y,….
The relation that an element x belongs to the set S is denoted by x  S (we read it: “x is an element of S”).  If the element y is not a member of the set S, we write y  S (we read it: “y is not an element of S”).
We consider that a set is given if all its members are known. The set named letters has a finite number of elements, hence we call it a finite set. On the other hand, the set named numbers has an infinite number of its elements. Therefore we call it an infinite set.
Some sets can be so long that we can not list all their members. In that case we define a set by giving a property or condition that all elements satisfy.
A = { x | x is each man who thinks he is clever and handsome }
Read this as "A is defined to be the set of x's such that x is each man who thinks he is clever and handsome". Instead of such that it is sometimes better to say for which or where.
The vertical line {..|...} used in this definition is called a constraint bar since only elements that satisfy the condition that follows it may be elements of the set. In fact there is no doubt about it: all elements that satisfy the constraint are members of the set.
A set has no duplicate elements. An element is either a member of a set or not. It cannot be in the set twice.
{1, 2, 3} is the same as the set {1, 3, 2, 3, 1}

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Basic Maths / Theory of sets

« on: March 31, 2016, 11:43:37 AM »

Once upon a time there was a gorilla. Then there came another gorilla. In a few days there were a lot of gorillas. They made a community. We can say that this community is one set that consists of its members. Gorillas are elements of the set. One intelligent man is not an element of such a set. Look at our Solar system. It consists of the Sun and planets around it. Our Solar system is a set that consists of its members. Earth is one of them.
A set is a collection of objects.
A set is definite if all its members are known. There are a lot of sets: a set of letters, a set of numbers....
letters = {a, b, c, ...x, y z}
numbers = {0, 1, 2, 3, ...}
Three points ... have the same meaning as etc. We use the symbol = and brackets {,} to denote the fact that specific elements belong to a set.

11

Basic Maths / Re: Number System

« on: March 31, 2016, 11:42:20 AM »

Fundamental Properties of  Real Numbers (R):

The Closure, Identity, Commutative, Associative and Distributive properties of the real numbers are important because they are the fundamental justification for many of the steps taken in algebraic procedures.

Property   Addition   Multiplication
Closure


Identity


Commutative


Associative


Distributive   If a and b are real then a+b is real

There exists a real number 0 such that a+0=0+a

If a and b are real then a+b=b+a

If a,b and c are real then (a+b)+c= a(b+c)

If a,b and c are real then a(b+c)=ab+ac
   If a and b are real then a.b is real

There exists a real number 1 such that a.1=a

If a and b are real then a.b=b.a

If a,b and c are real then (ab)c= a(bc)

12

Basic Maths / Re: Number System

« on: March 31, 2016, 11:41:45 AM »

Integers: Whole numbers and the opposites of whole numbers.
Rational Numbers: Numbers that can be written as a fraction (or ratio) of two integers.
Irrational Numbers:  Numbers that cannot be written as a fraction of two integers and are on the number line.
The numbers defined above are in some ways similar as well as different.
The numbers are similar in that they are all components in the real number system.
The numbers are different in their definitions.
Let's look at a few examples...

Integers   Rational   Irrational

5, -9, 0, 2, -16             
2/5,  7/9,  3/8,  2.3


Since integers can be written in fractional form they can also be considered rational numbers.  However, not all rational numbers can be integers!
The Real Number System is made up of all the points on the number line. Real Numbers are either integers, rational or irrational. (These are the subsets of the real number system.)

Since integers can be written in fractional form, integers can also be considered rational numbers.
 
The numbers shown here represent both rational and irrational numbers.
The integer, -2, is a rational number.
The decimal number 0.5 is also a rational number.
Pi ( ) ( 3.14) is a decimal number that, to our knowledge, has no end and cannot be expressed as a ratio of two integers. Therefore it is an irrational number.
Repeating decimals are also rational numbers. Take for example the repeating decimal  . This can be expressed as a ratio of two integers as 

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BBA Discussion Forum / Re: Notice for Final Exam, Spring 2016, 14 March 2016

« on: March 31, 2016, 11:34:22 AM »

Students of Uttara campus are also asked to follow this notice.

14

Business Administration / Principles of Total Quality Management

« on: March 27, 2016, 05:58:39 PM »

Total quality management represents a set of management principles that focus on quality improvement as the driving force in all functional areas and at all levels in a company. These principles are;

1.   The customer defines quality, and customer satisfaction is the top priority.
2.   Top management must provide the leadership for quality.
3.   Quality is a strategic issue and requires a strategic plan.
4.   Quality is the responsibility of all employees at all levels of the organization.
5.   All functions of the company must focus on continuous equally improvement to achieve strategic goals.
6.   Quality problems are solved through cooperation among employees and management.
7.   Problem solving and continuous quality improvement use statistical quality control methods.
8.   Training and education of all employees are basis for continuous quality improvement.

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Positive Bangladesh / পুরাকীর্তি সাত গম্বুজ মসজিদ এর সংক্ষিপ্ত বর্ণনা

« on: March 27, 2016, 05:35:57 PM »

ষোড়শ শতাব্দীতে প্রতিষ্ঠিত মোগল শাসনের ধারাবাহিকতায় যে স্থাপত্যরীতি প্রচলিত রয়েছে তারই উদাহরণ ‘সাত গম্বুজ মসজিদ’টি। ধারণা করা যায়, ১৬৮০ খ্রিস্টাব্দে নবাব শায়েস্তা খাঁ মসজিদটি নির্মাণ করেন। অন্য এক তথ্যে জানা যায়, নবাব শায়েস্তা খাঁর জ্যেষ্ঠপুত্র বুজুর্গ উদ্দিন (উমিদ) খাঁ এই মসজিদের প্রতিষ্ঠাতা। বর্তমানে, মসজিদটি প্রত্নতত্ত্ব অধিদপ্তরের তত্বাবধানে আছে।

আবস্থানঃ
ঢাকা শহরের মোহাম্মদপুর এলাকার সাত মসজিদ রোডে এই ঐতিহাসিক ‘সাত গম্বুজ মসজিদ’টি অবস্থিত। মসজিদটি প্রত্নতত্ত্ব অধিদপ্তরের তত্বাবধানে থাকলেও স্থানীয় মুসল্লিগণ সেখানে নিয়মিত নামাজ আদায় করেন।

মসজিদের বিবরণঃ
এর ছাদে রয়েছে তিনটি বড় গম্বুজ এবং চার কোণের প্রতি কোনায় একটি করে অনু গম্বুজ থাকায় একে সাত গম্বুজ মসজিদ বলা হয়। এর আয়তাকার নামাজকোঠার বাইরের দিকের পরিমাণ দৈর্ঘ্যে ১৭.৬৮ এবং প্রস্থে ৮.২৩ মিটার। এর পূর্বদিকের গায়ে ভাঁজবিশিষ্ট তিনটি খিলান এটিকে বেশ আকর্ষণীয় করে তুলেছে। পশ্চিম দেয়ালে তিনটি মিহরাব রয়েছে। দূর থেকে শুভ্র মসজিদটি অত্যন্ত সুন্দর দেখায়। মসজিদের ভিতরে ৪টি কাতারে প্রায় ৯০ জনের নামাজ পড়ার মত স্থান রয়েছে।

মসজিদের পূর্বপাশে এরই অবিচ্ছেদ্য অংশে হয়ে রয়েছে একটি সমাধি। কথিত আছে, এটি শায়েস্তা খাঁর মেয়ের সমাধি। সমাধিটি ‘বিবির মাজার’ বলেও খ্যাত। এ কবর কোঠাটি ভেতর থেকে অষ্টকোনাকৃতি এবং বাইরের দিকে চতুষ্কোনাকৃতির। বেশ কিছুদিন আগে সমাধিক্ষেত্রটি পরিত্যক্ত এবং ধ্বংসপ্রাপ্ত ছিল। বর্তমানে এটি সংস্কার করা হয়েছে। মসজিদের সামনে একটি বড় উদ্যানও রয়েছে। একসময় মসজিদের পাশ দিয়ে বয়ে যেত বুড়িগঙ্গা। মসজিদের ঘাটেই ভেড়ানো হতো লঞ্চ ও নৌকা। কিন্তু বর্তমান অবস্থায় তা কল্পনা করাও কষ্টকর। বড় দালানকোঠায় ভরে উঠেছে মসজিদের চারপাশ।