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

Assignment Help:

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.


Related Discussions:- De morgan''s laws - artificial intelligence

What factors influences the bus design decisions, What factors influences t...

What factors influences the bus design decisions? 1.  Data Location: Device selection, address of data with in device( track, sector etc) 2.  Data transfer: Amount, rate to

Implement a memory management system , There should be 1 server thread and ...

There should be 1 server thread and N client threads, where N is supplied by the user as a command line argument. The server opens a file called "all_requests.dat", the file has

Overcoming global issues in e-commerce, E-commerce advance tremendous chanc...

E-commerce advance tremendous chance by permitting industrialist to buy Materials at a low price internationally. Also they give companies the opportunity to sell to universal stor

Advantage of crc over simple checksum, Why can CRC detect more errors than ...

Why can CRC detect more errors than simple Checksum? There are two purposes a CRC can identify more errors than a simple Checksum. 1. Since an input bit is shifted by all th

the bias and standard error , A random variable (X) is modelled as an expo...

A random variable (X) is modelled as an exponentially distributed with mean 30 units. Simulate N = 50 samples from this distribution, and every sample must have m = 20 simulated va

Avantages of oopl in a programming language, Object oriented programming la...

Object oriented programming languages directly show the real life objects. The features of OOPL as inheritance, polymorphism, and encapsulation makes it strong.

What is anonymous file transfer protocol, What is Anonymous File Transfer P...

What is Anonymous File Transfer Protocol? Anonymous FTP: While a FTP client contacts a server, in that case, the daemon will ask for an account number or username and it

Explain ip address structure, Q. Explain IP Address Structure? Internet...

Q. Explain IP Address Structure? Internet addresses are divided in five types of classes. Classes were designated A through E. class A address space enables a small number of n

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd