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
Define the meaning of Registers and Counting? Registers: Group of flip-flops use for data storage. Counting: Another extremely important application of flip-flops is in dig

One of the most important competitive strategies for E-Businesses today is business process reengineering. BPR is more than automating business processes to make modest improvement

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

Explain about the Microsoft and the Netscape With the increasing competition between certain vendors especially the Microsoft and the Netscape, there have been a number of chan


Three state table buffers Three state table buffers: A bus system can be constructed with the help of three state gates instead of multiplexers. A three states gate is digital

The English existential construction involves so-called there-sentences such as these: (1)  There is a dog in the yard (2)  There were no children at the party (3)  There

list advantages of array

explain the various types of computer systems

In a two stage network there are 512 inlets and outlets, r=s=24. If the probability that a given inlet is active is 0.8, calculate: the switching elements Given: N =M =512,