
In Mathematics, a welldefined collection of definite objects is called a set. Sets *Is a collection of unique elements. *It is important that the such a collection is well defined. If there is any ambiguity, the collection is not a set. *George Cantor is regarded as the "Father of Set theory". *The concept of "Sets" is basic in all branches of mathematics. *It has proved to be of particular importance in the foundations of relations and functions, sequences, geometry, probability theory etc. *The study of sets has many applications in logic, philosophy, etc. Sets Notation: *It is indicated by list of its elements enclosed in {}. *It can be given names such as: A B C D F .............etc Example: Natural numbers less than 10 can be written in set notation as N = {1,2,3,4,5,6,7,8,9} A collection of "red sports cars" is a set. A collection of "good sports car" is not a set, since what is good for one person may not be good for someone else. * Let D represent the set of days of the week. Then D = {Sunday, Monday, Tuesday, Wednusday, Thursday, Friday, Saturday} We can use belong to symbol Î to indicate that something is in the set. Example: Monday Î D and is read as: Monday is a member of the set D But Holiday Ï D is read as Holyday is not a member of the set D Representation of Sets: There are two methods of representing a set. (i) Roster Method (ii) Set builder form Two special sets: Empty set or Null set Æ or {} A set which has no elements is called an empty set. Universal set represents U A set which has all the elements in the universe of discourse is called a universal set Other sets: Subset: A set A is a subset of a set B if and only if everything in A is also in B. In other words, a subset is a portion of a set. It is denoted by Ì or Í Superset: A superset is a set that includes other sets. It is denoted by É or Ê Example: A = {1,2,3} and B = {1,2,3,4,5,6,7,8}. Here A is a subset of B and B is superset of A. A Ì B then B É A Finite and Infinite Sets A set is finite if it contains a specific number of elements. Otherwise, a set is an infinite set. Examples : Finite set: Set of all natural numbers less than 5. Infinite set: Set of all natural numbers. Directions: Solve the following using set. 