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Class 11 maths revision notes sets

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SETS, RELATIONS & FUNCTIONS SETS, RELATIONS & FUNCTIONS SETS 2.2 Set-Builder Form 1. SET A set is a collection of well-defined and well distinguished objects of our perception or thought. 1.1 Notations The sets are usually denoted by capital letters A, B, C, etc. and the members or elements of the set are denoted by lowercase letters a, b, c, etc. If x is a member of the set A, we write x  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 belong to A, we write x, y  A. 2. REPRESENTATION OF A SET Usually, sets are represented in the following two ways : (i) Roster form or Tabular form (ii) Set Builder form or Rule Method 2.1 Roster Form In this form, we list all the member of the set within braces (curly brackets) and separate these by commas. For example, the set A of all odd natural numbers less that 10 in the Roster form is written as : A = {1, 3, 5, 7, 9} In this form, we write a variable (say x) representing any member of the set followed by a property satisfied by each member of the set. For example, the set A of all prime numbers less than 10 in the set-builder form is written as A = {x | x is a prime number less that 10} The symbol '|' stands for the words 'such that'. Sometimes, we use the symbol ':' in place of the symbol '|'. 3. TYPES OF SETS 3.1 Empty Set or Null Set A set which has no element is called the null set or empty set. It is denoted by the symbol I . For ex ...
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