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. 

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Negation Is The Consideration Of The Statement

Basic Concept Of Negation

To assert a statement is to say that it is true and to deny it is to say that, it is false. Negation is the consideration of the statement which may be either an assertion or denial. If p is a statement then ~ p (rear as not p) will be its Negation. But if ~ p is a statement then p will be its Negation which we can also express ~(~ p) p. The following Truth table shows how when p is true, ~ p is false and vice-versa is also there.

An electronic circuit showing this type of relationship is as follows:

The above circuits shows that the electronical impulse passes from S1 to S2 in case of p and it will pass to S2 (S2 bar) and not to S2 in case of ~ p.

Double Negation is positive which can be verified from the following Truth Table.

 

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Concept Of Logical Statements and Truth Table : Chapter 1

Introduction of Mathematical Logic

Logical statements deal with the binary logic used extensively it modern mathematics. Based on Boolean algebra, the logical statements introduce mathematical logic to the students. There is great relevance of these statements in modern mathematics because the basic philosophy behind the digital computers is based on digits 1 And 0. The binary codes and logical circuits used in computer employ signals of true or false. The two stable states of an electrical switching circuit are ON and OFF. With these a large number of mathematical operations are performed through suitably designed circuits.

Structure:

•          Logical Statements
•          Truth Table
•          Negation
•          Compounding
•          Negation of Compound Statements
•          Tautologies and Fallacies
•          Propositions
•          Algebra of Propositions
•          Conditional Statements
•          Biconditional Statements
•          Arguments
•          Joint Denial

Objectives:  After studying this chapter You should be able to Understand…..

1.  Logical statements, Truth table, Negation, Compounding, Negation of compounding statements, Tautologies and Fallacies, Propositions
2.   Algebra Of Propositions
3.   Conditional and Biconditional Statements
4.   Arguments and Joint denial

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