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

Explain open-systems interconnections architecture model, Q. Explain Open-s...

Q. Explain Open-systems interconnections architecture model The most common network architecture model is the open-systems interconnections (OSI). Figure shows the ISO (Intern

Discuss about the electronic computer, Discuss about the Electronic compute...

Discuss about the Electronic computer The first general function programmable electronic computer was the Electronic Numerical Integrator and Computer (ENIAC), built by John V

Explain segment registers in bus interface unit, Q. Explain Segment Registe...

Q. Explain Segment Registers in bus interface unit? These are very significant registers of CPU. Why? We will answer this later. In 8086 microprocessor memory is a byte organiz

What are the main aspects available in all word processors, What are the Ma...

What are the Main aspects available in all word processors -  Ability to set page size and page orientation -  Ability to change font size and font style (for example Arial,

What is computer communications networks, Q. What is Computer communication...

Q. What is Computer communications networks? Computer communications networks are the outcome of a combination of computers and telecommunication products. An interconnected gr

Explain the feasibility study, Explain the Feasibility Study This inclu...

Explain the Feasibility Study This includes writing a report to convince management of the merits of adopting proposed new system. Some features of the study comprise: T

EME, How can i made Carnot engine

How can i made Carnot engine

Explain chomsky classification of languages, Explain chomsky classification...

Explain chomsky classification of languages with suitable examples Ans: Any language is appropriate for communication provided the syntax & semantic of the language is termed t

Characteristics of the id process, The following is taken from the first ed...

The following is taken from the first edition of the Set Book. We have included this because we find these characteristics helpful. We will refer to them later. In addition to t

Drawback of the system using disk caching, Q. Drawback of the system using ...

Q. Drawback of the system using disk caching? The main drawback of the system using disk caching is risking loss of updated information in event of machine failures like loss o

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