SETS (Collection of well defined objects)

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                 INTRODUCTION

In our mathematical language, everything in this universe, whether living or -living is called an object.

A given collection of objects is said to be well defined, if we can definitely say either a given particular object belongs to the collection or not. 

SET: A well-defined collection of objects is called a set. The objects in a set are called its members or elements.

We denote sets by capital letters A, B, C, X, Y, Z, etc. If a is an element of a set A, we write, a e A, which means that a belongs to or that a is an element of A.

If a does not belong to A, we write, a € A.

ILLUSTRATIONS

(I) The collection of all vowels in the English alphabet is the set containing five elements, namely a, e, i, o, u. f. 

(I I)The collection of all even natural numbers less than 10, is the set containing the numbers 2, 4, 6,8. 

(I I I) The collection of all prime numbers less than 20, is the set containing the numbers 2357111317 19. 

(I V) We denote the sets of all natural numbers, all integers, all rational numbers and all real numbers by N, Z, Q and R respectively.

(V) The collection of all beautiful girls of India is not a set, since the term beautiful' is vague and it is not well defined. Similarly, 'rich persons', 'honest persons', 'good players', 'old people', 'young men', etc., do not form sets.


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