Venn Diagrams are named after English Logician John Venn

The Venn Diagrams are named  after  English  Logician  John  Venn (1834-1923)  to present  pictorial  representation. The Universal Set, say  U or X is denoted by a region enclosed by a ractangle and one or more sets say, A, B, C are shown through circuits or closed curves within these rectangles. These circuits or closed curves intersect each other if there are any common elements amongst them, If there are no common elements then they are shown separately as disjionts.

Several set relations can be easily shown by these diagrams. These are useful to illustrate the set relations, such as the subset, set relations and the set-operations such as intersection, union, complemention, etc. by using regions in aplane to indicate sets. But Venn Diagrams (also known as Venn Euler Diagrams) can not be used to prove any statements regarding sets, just as geometric figures can not be used to prove geometric theorems. They are more aids for searching appropiate proofs.    

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Theory Of Sets

Introduction:
The statements in the first chapter were concerned with individual objects. In Set we deal with a group of objects which can be defined in terms of their distinctive characteristic, magnitudes, etc. However, both the logical statements and sets belong to the same class. In the case of logical statements, we had three Boolean operators, like Conjunction, Disjunction and Negation. In set theory these are called as Intersection ∩ , Union ∪ and Complementation { } respectively.
Both they play an important role in modern Mathematics. The logical statements and Truth tables help in designing the circuits to perform Boolean Operations, the sets are of much wider application, especially they help in preparing the programme for feeding into the machine. In almost whole of the Business Mathematics the set theory is applied in one form or the other.

Structure:

• A Set
• Elements of a Set
• Method of Describing a Set
• Types of Set
• Venn Diagram
• Operations on Sets
• Intersection of Sets
• Union of Sets
• Complement of Sets
• De-Morgan’s Law
• Difference of two Sets
• Symmetric Difference
• Algebra of Sets
• Duality
• Partition of a Set
• Regrouping of the Sets
• Number of Elements In Finite Sets
• Ordered Pair
• Cartesian Product
• Set Relations
• Properties of Relations
• Binary Relations
• Functions Or Mappings
• Types Of Mappings

Objectives: After studying this chapter, You should be able to understand

• Set, Elements of a Set, Method of Describing a Set, Types of Set, Venn Diagram, Operations on Sets
• Algebra of Sets
• Cartesian Product
• Set Relations and its Relations
• Binary Relations, Functions and Mappings

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