De morgan''s laws - artificial intelligence, Computer Engineering

De Morgan's Laws

Continuing with the relationship between  and , we can also use De Morgan's Law to rearrange sentences involving negation in conjunction with these connectives. Actually, there are 2 equivalences which taken as a pair are called De Morgan's Law:

¬(P Q) ≡ ¬P ∨¬Q

¬ (P ∨ Q) ≡ ¬P  ¬Q

These are essential rules and it is good spending some time thinking regarding why they are true.

Contraposition

The contraposition equivalence is following:

P -> Q ≡ ¬Q -> ¬P

At first, this can seem a little strange because it seem that we have said nothing in the first sentence regarding ¬Q, soin the second sentence how can we infer anything from it? However, imagine we know that P implies Q, and we saying that Q was false. In this case, if we were to imply that P was true because we know that P implies Q, we also know that Q is true. But Q was false .So we cannot possibly denote that P is true, which means that we ought to imply that P is false (because we are in propositional logic, so P might be either true or false). This argument shows that we may replace the first sentence by the second one, and it is left as aworkout to construct a similar argument for the vice-versa part of this equivalence.

Posted Date: 10/2/2012 8:04:29 AM | Location : United States







Related Discussions:- De morgan''s laws - artificial intelligence, Assignment Help, Ask Question on De morgan''s laws - artificial intelligence, Get Answer, Expert's Help, De morgan''s laws - artificial intelligence Discussions

Write discussion on De morgan''s laws - artificial intelligence
Your posts are moderated
Related Questions
Input a list of positive numbers (terminated by 0) into an array. Find the largest number in the array, and into the result. Use a subprogram to input the numbers, a function to fi

Network Properties There are many properties are associated with interconnection networks:- 1) Topology: It signify how the nodes a network are organised. A variety of top


What are the different ways in which a thread can be cancelled?  Cancellation of a target thread may occur in two different scenarios: Asynchronous cancellation: One thre

Write a class encapsulating the concept of a circle? I have been working on this program for awhile and this is all I have so far... What are my flaws in the program besides not ha

Double Negation : All parents are forever correcting their children for the find of double negatives,  there we have to be very alert with them in natural language like: "He d


SET SCREEN With SET SCREEN the present screen simply specifies the next screen in the chain , control branches to this next screen  as soon as the current screen has been proce

What is the use of hypertext links in Internet access? Use of Hypertext links in Internet access: From the user’s view point, the Web comprised a vast, worldwide collecti

ERP usage in real world