What is Set? Set : A set is a well -defined collection of objects. Well-defined means a collection of object in the sense that we can definitely Decide whether a given particular Object belongs to a given collection or not. For example ,we can say that the river nile does not belong to collection of rivers of India. On the other Hand the river ganga does belong to this collection
For example: (i) odd natural number less then 10, i.e., 1,2,5,7,9 (ii) The vowels in English alphabet ,namely, a,e,i,o,u (iii)Various kinds of triangles equilateral triangle isosceles triangle (iv) The solution of the equation : x2-5x+6-0,viz ,2 and 3 scalene triangle
Not well -defined 1)Set of good students (what is good student is not defined) 2)Set of young people in a city ( What is age limit of young people is not defined) .
Q.Which of the following are sets? Justify your answer (i)The collection of all boys in your class. (ii)The collection of all natural number less then 100. (iii)A collection of most dangerous animal of the world.
Solution (i)The collection of all boys in your class is a well-defined collection because you can definitely identify a boy who belongs to this collection. Hence,this collection is a set (ii)The collection of all natural numbers less than 100 is a well-defined collection because one can definitely identify a number that belongs to this collection. Hence, this collection is a set. (iii)The collection of most dangerous animals of the world is not a well-defined collection because the criteria for determining the dangerousness of an animal can vary from person to person. Hence, this collection is not a set.
Set Notation There is a fairly simple notation for sets. We simply list each element (or "member") separated by a comma, and then put some curly brackets around the whole thing three dots means goes on forever (infinite) element element element ("element" or "member" mean the same thing)
Key points (i) Objects ,elements and member of a set are synonymous term. (ii) Sets are usually denote by capital letters A,B,C,etc. (iii) The elements of set are represented by small letter a, b,c,d ,etc.
If a is an element of a set A ,we say that " a belongs to A" the Greek symbol E(epsilon) is used to denote the phrase 'belongs to', Thus we write a e A If b is not an element of a set A ,we write b A and read "b does not belong to A".
Q. Let A-{1,2,3,4,5,6j. Insert the appropriate symbol e or in the blank spaces: