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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