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CONCEPT OF A SET

CONCEPT OF A SET. The concept of set is not difficult to understand as it is used in our daily life. In our routine life, we use names for collection of certain objects. For e.g. Class of students, a herd of sheep, a week of seven days, a bunch of keys and a team of players etc. INTRODUCTION.

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CONCEPT OF A SET

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  1. CONCEPT OF A SET • The concept of set is not difficult to understand as it is used in our daily life. In our routine life, we use names for collection of certain objects. For e.g. Class of students, a herd of sheep, a week of seven days, a bunch of keys and a team of players etc.

  2. INTRODUCTION • The concepts about sets were first introduced by George Cantor in the nineteenth century and in the twentieth century these concepts in the form of set theory interrelated, integrated and united many branches of Mathematics. Set theory is continually becoming the language of Mathematics.

  3. THE WORD SET • There are so many words in English language that we can use for a collection of well-defined and distinct objects. In the language of Mathematics we can say • The set of all articles in a classroom. • The set of birds that can fly. • The set of books in the cupboard.

  4. SET NOTATION • We give names to the sets. We use capital letters of the English alphabet A, B, C, D,……………….., X, Y, Z to denote the sets. The curly brackets { } are sometimes called "set brackets" or "braces".

  5. MEMBERS OR ELEMENTS OF A SET • This means that something which belongs to a collection or a group is called its member or element. Those things which belong to a set are called its ELEMENTS or MEMBERS.

  6. PROPERTIES OF A SET • Set must be well defined. • All the members of a set must be distinct and distinguishable. • A Member in a set is written only once i.e. it is not repeated. • There is no restriction on the number of elements of a set. • The elements of a set may be written in any order

  7. NOTATION FOR DENOTING WHETHER AN OBJECT IS OR ISNOT A MEMBER OF SET • E is a notation for denoting the membership of an element in a set . • Similarly E/is a notation for denoting the fact that some object is not an element of a set.

  8. METHOD FOR REPRESENTING A SET • Usually there are two methods of representing a set. (i) Tabular Method. (ii) Descriptive Method.

  9. TABULAR METHOD • In this method all the members of a set or their figures are tabulated within the braces, separated by commas. For e.g. A={Tahir, Khalid, Shahid} B={1,2,3,4,5,6,7,8} C={a,b,c,d,e} D={1,2,3,4,…………….,500}

  10. DESCRIPTIVE METHOD • In this method the members of a set are described by stating a property or properties that they satisfy. This method is called descriptive method. The use of braces is not necessary in this method.

  11. EMPTY SET When there is no tea in the cup, we say the cup is empty. When there is no student in the class we say the classroom is empty. Similarly when there is no element in the set we say the set is empty. So, A set having no element at all is called an empty set.

  12. UNION OF A SET • The union of two sets A and B is the set which consists of all the elements of both the sets A and B. Symbol U is used to denote union. The union of A and B is denoted by AUB and is read A union B.

  13. INTERSECTION OF SETS • The intersection of two sets A and B is the set which consists of those elements which are common to both A and B .

  14. COMMUTITIVE PROPERTY OF UNION AND INTERSECTION • If A and B are any two sets, then AUB=BUA • If A and B are any two sets, then A ∩ B = B ∩ A.

  15. INSTRUCTIONAL STRATIGIES • I will encourage the students to do their mental calculations in order to enhance their mental calculation calculations skills • I will provide them different tips as a tool to involve them so that they can enjoy maths as a fun. • I will try my level best to create such activities that my students must produce interest in the topic instead of getting bored or having fear in mathematics.

  16. CHALLENGES Children have weak calculation skills so they get distracted. Some students have slow conceptual skills. Some parents are not involved with the child’s progress and least bothered. SOLUTIONS I will provide them extra class and give them extra time so that their calculation skills be improved. They will be provided with extra worksheets so that they can enhance their conceptual skill. Parents will be guided that mathematical skills are very necessary to their child’s mental growth. SOLUTIONS TO ANTICIPATION CHALLENGES

  17. CONCLUSION By implementing my newly acquired 21st century teaching approaches students will be encouraged and empowered and will be appreciated to gain a better knowledge of mathematics.

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