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

Telnet services, java program for implementation of telnet services

java program for implementation of telnet services

The mercantile process model, The mercantile process model consists of whic...

The mercantile process model consists of which of the pahase(s): The pre-purchase phase. Purchase consummation phase. Post-purchase Interaction phase.

Scanf function, How can the maximum field width for a data item be specifie...

How can the maximum field width for a data item be specified within a scanf function? When the program is executed, three integer quantities will be entered from the standard i

What is decision support system and describe its components, Q. What is a D...

Q. What is a DSS and Describe its components? A decision support system (DSS) is a highly flexible and interactive IT system that is designed to support decision making when t

Asembly language programming, Ask question #Minimum Write a program to mask...

Ask question #Minimum Write a program to mask bits D3D2D1D0 and to set bits D5D4 and to invert bits D7D6 of the AX register. 100 words accepted#

Raid and data stripping, Explained RAID? Ans: High performance devices ...

Explained RAID? Ans: High performance devices tend to be costly. So we can gain very high performance at a reasonable cost using a number of low-cost devices operating in paral

What are the advantages of carrying out simulations, What are the Advantage...

What are the Advantages of carrying out simulations -  saves cost (instead of doing the real thing) -  Safer (scenarios tried out on the simulation first before used in real

Define synchronization latency problem, Q. Define Synchronization Latency P...

Q. Define Synchronization Latency Problem? If two simultaneous processes are executing remote loading then it's not recognized by what time two processes will load as issuing p

What is the necessity of an interface, What is the necessity of an interfac...

What is the necessity of an interface?  Any device that has to be linked to a CPU requires an interface. This takes care of the mismatch in speed, data and electrical character

Macroscopic and microscopic approaches - thermodynamics, Macroscopic and Mi...

Macroscopic and Microscopic approaches - Thermodynamics: Thermodynamic studies are undertaken by following two different approaches.  l. Macroscopic approach (Macro mean big)

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