2.2 SET

A set is a well defined collection of distinct objects. The objects in a set are called elements. Sets are written by enclosing all its elements between the brackets { }.

For example, when we want to write a set of first five prime numbers, it can be written as {2,3,5,7,11} and set of incisors = {central incisor, lateral incisor}

Do This

Write the following sets

  • 1) Set of the first five positive integers.

  • 2) Set of multiples of 5 which are more than 100 and less than 125

  • 3) Set of first five cubic numbers

  • 4) Set of digits in the Ramanujan number


    • 2.2.1 ROSTER FORM AND SET BUILDER FORM

    It is difficult to express a set in a long sentence. Therefore, sets are generally denoted by capital letters of English alphabet A, B, C.....

    For example, M is the set of molars among our teeth.

    We can write this set as M={first molar, second molar, third molar}.

    Let us look at another example. Q is the set of quadrilaterals with at least two equal sides. Then, we can write this set as

    Q ={square, rectangle, rhombus, parallelogram, kite, isosceles trapezium, dart}

    Here, we are writing a set by listing the elements in it. In such case, the set is said to be written in the “roster form”.

    In the above two examples, let us discuss belongingness of the elements and its repre- sentation. Suppose, if we want to say “second molar is in the set of molars”, then we can repre- sent this as “second molar belongs to M”. And we read this as "second molar belongs to set M"

    Can we say “rhombus belongs to Q” in the above example of set of quadrlaterals? How do you read this?

    Does “square” belong to the set M in the above examples?

    Then, how do we denote this? When we say “ square is not in the set M”, we denote as “square Ï M”.

    And we read this as "square does not belong to the set M".

    Recall from the classes you have studied earlier that we denote natural numbers by N,set of integers by Z, set of rational numbers by Q, and set of real numbers by R.





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