SETS A set is a collection of objects of any kind which are collected together perhaps because of some property they have in common. Examples: The collection of numbers used for counting, the collection of all paintings of an artist. Mainly the objects of a set are required to be “well defined”. The objects which make up a set are called its members or elements. If the number of elements in a set is finite is called as finite set. Sets having infinitely many elements are called infinite sets. Set having only one element is called a singleton set.

SETS Continued…. For describing a set, two methods are commonly used: 1.The Tabulation Method 2.The Rule Method In tabulation method, all elements of a set are written down within braces(flower brackets) if there are too many elements ,the first few elements are written down in such a way as to indicate clearly what others are. In rule method ,we specify the set by stating a characteristic property which all the elements of the set possess and which no other object possesses. Example: If ‘S’ is the set of all positive odd integers , then S can be described as shown……

SETS Continued…. S={1,3,5,7……} S={x/x is a positive odd integer} The tabulation method is used in the first of above descriptions of S and the rule method is used in the second. The first description is read as:” S is the set consisting of the elements 1,3,5,7….” and the second description is read as :”S is the set of elements ‘x’ such that ‘x’ is a positive odd integer”. In the second description , the vertical line within the brackets stands for “such that”. The singleton set consisting of the element a is described by the tabulation method and is denoted by {a}.