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.    

Read more...

Definition Of Set And Elements Of A Set

A Set:
A set is a collection of well-defined and well-distinguished objects. From a set it is possible to tell whether a given object belongs to a set or not. The following are some illustrations of a set:

• The possible outcomes in the toss of die
• The Integers from 1 to 100
• The vowels in English alphabets

The basic characteristics of a set are that it should be well-defined; its objects or elements should be well- distinguished for easy recognition by description.

Elements Of A Set:
The object that makes up a set are called the members or elements of the set. It is almost a convention to indicate sets by capital letter, like A, B, C or X, Y, Z while the elements in the set by smaller or lower case letters, viz.., a, b, c or x, y, z. Now, to indicate that a particular element or object “ belongs to a set “ or “ a member of the set ” we use the Greek symbol capital epsilon ∈.
For example if x is the member of a set A, We shall indicate it symbolically as:
x∈A,i.e.,x is a member Or an elements of the set A

Read more...

Negation of Compound Statement

Today i Will write about Negation of Compound Statement. Here you will find the clear concept of Negation of Compound Statement and its Different Functions. When a compound statement is negated its connective changes from AND to OR and from OR to AND. For example,

We can say that the inversion of a function of several terms is obtained by inverting the individual terms and changing the connectives. This is the famous De Morgan’s theorem or law. It is very helpful in simplifying and rearranging the terms of a Boolean function which is sometimes better amenable to certain specialized operations. The truth of the De Morgan’s law can be verified from the following truth table:

The truth values of columns 4 and 7 are alike which proves the theorem.
The following are some relations based on the above law which can be verified by preparing truth tables:

Example: 1. Let p be the statement “the south-west monsoon is very good this year” and q be the statement “the rivers are rising”. Give the verbal translations for (a) and verify the statement (b).

Solution: 
(a)

1. The south-west monsoon is very good but the rivers are not rising.
2. It is not true that the south-west monsoon is not very good or the rivers are not rising. We can also state that the south-west monsoon is very good and the rivers are rising.

(b) The statement is false because if x2>1 then x>1 OR x<-1

So dear i think you understand this article very much. Best Of Luck. 

Read more...

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.

Read more...