Set Theory for GMAT

Description :

SETS

• "Set" is synonymous with the words: "collection";, "aggregate", "class" and is comprised of elements/objects/members.
• The following are some examples of sets:
• The collection of vowels in English Alphabets.
• The collection of all past Presidents of the Indian Union.
• The weights of all the students of a class.

DEFINING A SET :A set is a collection of well defined entities, objects or elements. OR A set is a group of one or more elements with common characteristics. OR A set is a collection of distinct, unordered objects. Sets are typically collection of numbers. So, a set may contain any type of data (including other sets).

DESCRIBING A SET: A set is described by listing elements, separated by commas, within brackets. For example: A set of vowels of English Alphabet may be described as: {a, e, i, o, u} A set of even natural numbers can be described as: {2, 4, 6, 8,…} Note: The order in which the elements are written makes no difference. Also, repetition of an element has no effect. For example {1, 2, 3, 2} is the same set as {1, 2, 3}. DESCRIBING A SET

FINITE SET: A set is called a finite set, if its elements can be counted and the process of counting terminates at a certain natural number say, ‘n’. Example: {1, 2, 3, 4, 5} , {1, 2, 3, 4,………..up to 100}

INFINITE SET :: A set which is not finite or in other words, a set in which the process of counting does not terminate is an infinite set. Example: Set of natural numbers, or {2, 4, 6, 8, 10,…………………. } set of even numbers or {1, 3, 5, 7, 9,……………………} set of odd numbers.

EQUAL SETS : Two sets A and B are said to be equal, if every element of A is a member of B, and every element of B is a member of A. If sets A and B are equal, we write A = B . Similarly, Unequal sets: When they are not equal or there exists at least one distinct element between these two sets. We write: A  B, when A and B are not equal. Let A = {1, 2, 5, 6} and B = {5, 6, 2, 1}. Then A = B because each element of A is an element of B and vice – versa.

UNIVERSAL SET : There happens to be a set ‘U’ that contains all the elements under consideration. Such a set is called the universal set. For example : A = {1, 2, 3, 4, 5), B = {4, 5, 6, 7, 8, 9 }. We can say that they are both contained in their universal set, which is a set of natural numbers. In plane geometry, the set of all points in the plane is the universal set.

Courtesy:- Slideshare.com