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 is high level formatting, Q. What is High level formatting? In any...

Q. What is High level formatting? In any disk system the space at some time in use would become discarded and therefore will be free for other application. Operating system ass

What are the steps involved in designing, Before getting into the design th...

Before getting into the design the designer should go by the SRS prepared by the System Analyst. The main tasks of design are Architectural Design & Detailed Design. In Arch

An example of load-store optimization using expression trees, Give LOAD-STO...

Give LOAD-STORE optimization based on expression trees for the expression (A+B)/(C-D). LOAD-STORE optimization based on expression trees for the expression (A+B)/(C-D) is given

Explain the random scan and raster scan displays, Define Random scan/Raste...

Define Random scan/Raster scan displays?  Random scan is a method in which the display is made by the electronic beam which is directed only to the points or part of the screen

List the various file attributes, List the various file attributes. A f...

List the various file attributes. A file has certain other attributes, which differ from one operating system to another, but typically consist of these: Name, identifier, type

Describe characteristics needed for an e-commerce server, Describe the addi...

Describe the additional characteristics needed for an e-commerce server? E-commerce services need dynamic configuration abilities and seasonal and every day service configurat

Convert the following into sop form, Convert the following into SOP form ...

Convert the following into SOP form 1. (A+B) (B'+C) (A'+ C) 2. (A'+C) (A'+B'+C') (A+B') 3. (A+C) (AB'+AC) (A'C'+B)

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