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 overflow and underflow case in single precision, What is overflow, ...

What is overflow, underflow case in single precision(sp)? Underflow-In SP it means that the normalized representation needs an exponent less than -126. Overflow-In SP it mea

What are the features of cisc processors, What are the Features of CISC Pro...

What are the Features of CISC Processors The standard features of CISC processors are listed below:  CISC chips have a large amount of dissimilar and complex instructions.

Explain about mmx architecture, Explain about MMX architecture MMX arc...

Explain about MMX architecture MMX architecture introduces new packed data types. Data types are eight packed, consecutive 8-bit bytes; four packed, consecutive 16-bit words;

Excess 3 codes, Explain Excess 3 Codes Ans. Excess 3 Codes 1....

Explain Excess 3 Codes Ans. Excess 3 Codes 1. This is the other form of BCD code. All decimal digits are coded in 4 bit binary code. 2. The code for all decimal di

What is internet address, Addresses are basically for virtually everything ...

Addresses are basically for virtually everything we do on Internet. The IP in TCP/IP is a mechanism for providing addresses for computers on Internet. Internet addresses have two f

Assembly Language, Write an assembly program to simulate a microwave

Write an assembly program to simulate a microwave

Characters in vi editor, What is the command used to replace many character...

What is the command used to replace many characters in Vi Editor? Ans) For replace most of the character in vi editor press esc key and then press R for change many character.

How much CMOS circuits consume power, CMOS circuits consume power ? An...

CMOS circuits consume power ? Ans. As in CMOS one device is ON and one is Always OFF therefore power consumption is low or can say less than TTL.

Illustrate about sharing of structure and behaviour, Illustrate about Shari...

Illustrate about Sharing of Structure and Behaviour  One of the reasons for the popularity of object-oriented techniques is that they promote sharing at different levels. Inher

Explain working of jaz drive, Q. Explain working of Jaz Drive? Jaz Dri...

Q. Explain working of Jaz Drive? Jaz Drive: Jaz drive is a well-liked drive with 2GB and unleashes creativity of professionals in graphic design and software development, pub

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