Methods of writing sets

Methods of writing sets
Standard 9
Maharashtra State Board, India

1. Chapter 1 sets Vaibhav Zade, Navpratibha High School, Nagpur Topic Methods of writing sets Navpratibha Study Forum

2. Navpratibha Study Forum Vaibhav Zade, Navpratibha High School, Nagpur There are two methods of representing or writing a set ( i) Listing Method or Roster Method ( ii) Rule Method or Set Builder Form

3. 3 2 Vaibhav Zade, Navpratibha High School, Nagpur We write all the elements of a set in curly bracket . Navpratibha Study Forum Listing Method or Roster Method Each of the elements is written only once and separated by commas. The order of an element is not important but it is necessary to write all the elements of the set . In listing or roster method , all elements of a set are listed. 1

4. A = { M, A, T, H, E, M, A, T, I, C, S } A = { M, A, T, H, E, I, C, S } Vaibhav Zade, Navpratibha High School, Nagpur i) The set of all the letters in word ‘MATHEMATICS’. Navpratibha Study Forum Let see an example A T A T M M ii) The set of odd numbers between 1 and 10 O = { 3 , 5, 7, 9 } or O = { 9 ,7, 5, 3 } iii) The Set of multiples of 7 B = { 7, 14, 21, 28, 35, 42, . . . . } iv) The set of all vowels in the English alphabet V = { a, e, i, o, u } v) The set of all natural factors of 42 F = { 1, 2, 3, 6, 7, 14, 21, 42 } In roster form, an element is not generally repeated

5. Vaibhav Zade, Navpratibha High School, Nagpur Navpratibha Study Forum Rule Method or Set Builder form Instead of writing the list of elements, we use a variable. In rule method or set builder form, we describe the set by indicating properties of elements 3 2 1 Variable is followed by a vertical line | or colon : Variable is described by the common property of elements. All the elements of a set possess a single common property which is not possessed by any element outside the set.

6. Vaibhav Zade, Navpratibha High School, Nagpur i) The set of all natural numbers between 1 and 10. Navpratibha Study Forum Let see an example A = { x | x N, 1 < x < 10 }   set A is the set of all ‘ x ’ , such that , ‘ x ’ is a natural number, between 1 and 10 . We read the set as follows : A { } | 1 < x < 10 x x N   Listing Method A = { 2, 3, 4, 5, 6, 7, 8, 9 }

7. Vaibhav Zade, Navpratibha High School, Nagpur Set Builder form or Rule Method Navpratibha Study Forum Let see some examples Listing Method or Roster Method S = { 1, 4, 9, 16, 25, 36, . . . } S = { x | x is a square of natural numbers } 1. or S = { x | x = n 2 , n N }   2 . Set of letters of word ‘PRINCIPAL’ A = { P, R, I, N, C, A, L } A = { y | y is a letter in word ‘PRINCIPAL’ } 3. C = { . . ., - 6, -4, -2, 2, 4, 6, . . . } C = { a | a I , a is an even number }   4. G = { - 7, 7 } G = { x | x I , x = }  

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