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{SETS} CHAPTER CLASS 7TH || ML AGGARWAL CHAPTER 5 | EXERCISE 5.1 SOLUTION
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In our day-to-day life, we have to deal with collections of objects (or things). For example, consider the following collections:
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(i) collection of all students of your class whose weight exceeds 40 kg.

(ii) collection of all odd natural numbers less than 20 i.e. of the numbers 1,3,5,7, 9, 11, 13, 15, 17, 19.

(iii) collection of first six letters of the English alphabet i.e. of the letters of a, b, c, d, e, f.

( iv) collection of all months of a year.

(v) collection of first seven whole numbers which are multiplies of 3 i.e. of the numbers 0, 3, 6, 9, 12, 15, 18.

(vi) collection of all rivers of India.

(vii) collection of prime factors of 420 i.e. of the numbers 2, 3, 5, 7.

(viii) collection of all planets of the sun.

Note that each one of the above collections is a well defined collection of objects.

By a 'well defined collection of objects' we mean that given a collection and an object, it should be possible to tell beyond doubt whether the object belongs to the collection or not.SET
Sets 103

Any well defined collection of objects is called a set.

The objects which belong to the set are called its members or elements.

Each one of the above collections is a set.

Now, consider the following collections:

1) collection of all hard working students of your class. (

It is not a well defined collection because people may differ on whether a student of your class is hard working or not.

(ii) collection of reputed schools of India. It is not a well defined collection because people may differ on whether a

school of India is reputed or not.

(iii) collection of five months of a year.

It is not a well defined collection because it is not known which five months of a year are to be included in the collection.

Each of the above collections is not a set.

Note that the elements of a set may be objects, persons, numbers, letters or any things. Moreover, the elements of a set need not be alike.

Notation

The sets are usually denoted by capital letters A, B, C etc., and the members of a set are

denoted by small letters x, y, z etc.

If x is a member of the set A, we write x e A (read as 'x belongs to A') and if x is not a member of the set A, we write x A (read as 'x does not belong to A). If x and y both are members of the set A, we write x, y € A

Representation of a set

A set can be represented by the following methods:

(1) Description method

(ii) Roster method or tabular form

(iii) Rule method or set builder form.

Description method

In this method, we make a (well defined) description of the elements of the set and this description of elements is enclosed in curly brackets.

For example:

(1) The set of whole numbers less than 10 is written as (whole numbers less than 10).

Note that 0 € (whole numbers less than 10) while 10 e (whole numbers less than 10).

(ii) The set of even integers is written as (even integers). Note that -8 € (even integers) while 5 € (even integers).

(iii) The set of colours of rainbow is written as (colours of rainbow). Note that blue € (colours of rainbow) while black (colours of rainbow).
Roster method or tabular form

In roster method or tabular form, we list all the members of the set and separate these by commas. The list is enclosed in curly brackets.

(i) The set A of even whole numbers less than 10 in the roster method is written as A = (0, 2, 4, 6, 8).

Note that 0, 6 e A while 10 A.

(ii) The set V of months of a year whose name begin with a vowel in tabular form is written as

V = {April, August, October).

(iii) The set D of all days of a week in the roster form is written as

D = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday) (iv) The set P of consonants in the word KOCHIN in the roster form is written a P= {K, C, H, N}.

For example:

Rule method or set builder form

In rule method or set builder form, we write a variable (say x) representing any member of the set followed by a property satisfied by each element of the set and enclose it in curly brackets. If A

is the set consisting of elements x having property p, we write A = {xx has property p}

which is read as 'the set of elements x such that x has property p'. The symbol '|' stands for the words 'such that'. Sometimes, we use the symbol ':' in

place of the symbol '|'.

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