real numbers. The symbols for the special sets given above will be referred to throughout this text. Again the collection of five most renowned mathematicians of the world is not well-defined, because the criterion for determining a mathematician as most renowned may vary from person to person. Thus, it is not a well-defined collection.
We shall say that a set is a well-defined collection of objects. The following points may be noted : Objects, elements and members of a set are synonymous terms. Sets are usually denoted by capital letters A, B, C, X, Y, Z, etc. (iii) The elements of a set are represented by small letters a, b, c, x, y, z, etc.
If a is an element of a set A, we say that “ a belongs to A” the Greek symbol ∈ (epsilon) is used to denote the phrase ‘ belongs to ’. Thus, we write a ∈ A. If ‘ b ’ is not an element of a set A, we write b ∉ A and read “ b does not belong to A”. Thus, in the set V of vowels in the English alphabet, a ∈ V but b ∉ V.
In the set P of prime factors of , ∈ P but ∉ P. There are two methods of representing a set : Roster or tabular form Set-builder form. In roster form, all the elements of a set are listed, the elements are being separated by commas and are enclosed within braces { }. For example, the set of all even positive integers less than is described in roster form as { , , }.
Some more examples of representing a set in roster form are given below : (a) The set of all natural numbers which divide is { , , , , , , , }. SETS A Note In roster form, the order in which the elements are listed is immaterial. Thus, the above set can also be represented as { , , , , , , , }. (b) The set of all vowels in the English