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...

Truth table : Truth value of a compound statement constituting several statements

Definition Of Truth Table

Truth table is a table indicating the truth value of a compound statement constituting several statements. The statements are compounded by various connectives e.g. …… AND, OR & NEGATION etc. each one has a significance and therefore the truth of compound statement has to be considered taking these into considerations.

• A truth table has a number of columns and rows. The number of columns depends upon the number of constituent elements and how involved over their relationships. 

• The initial columns, two or three depending on the constituent statements. These give all possible combinations of the constituent statements.

• The remaining columns are the output columns giving the truth values of the compound statement as a function of certain relationship between constituent statements.

• The number of rows in a truth table is determined on the basis of the constituent statements. In case of 2 constituent statements, there are 4 rows and for 3 constituent statements, there are 8 rows.

The truth table is very useful in finding out the validity of an equivalence relation between function. For practical purpose, they help in designing and testing the electronic circuits to perform a given operation based on a certain relationship.

Read more...