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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Clear Concept of Compounding : What is Compound ?

Definition of COMPOUND

The method of combining statements is known as compounding; two or more constituent statements when combined into a joint statement is known as a compound statement. The compound connectives used for the purpose are AND, OR & NOT. Actually the Boolean Algebra recognizes only three operations by which a machine manages all other operations. Other connectives are also converted into these simple operators. The truth value of a compound statement will depend on the truth of the constituent statements. Compounding is done mainly through conjunction and disjunction.

• Conjunction:

• Disjunction:

I Will describe about conjunction and disjunction in my next post.

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