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

Which approaches not require knowledge of the system state, Which approache...

Which approaches do not require knowledge of the system state? Ans. Deadlock detection, deadlock prevention and deadlock avoidance; none of the given require knowledge of the s

Decomposition model of parallel programming, The PVM system supports functi...

The PVM system supports functional and data decomposition model of parallel programming. It attaches with C, C++, and FORTRAN. The C and C++ language bindings for the PVM user inte

Differentiate between public key and secret key encryption, What are the di...

What are the different between Public Key Encryption and Secret Key Encryption? Differentiate between Public Key Encryption and Secret Key Encryption: A cryptographic sys

Ds, explain about relations

explain about relations

Determine about the web authoring tools, Web authoring tools CGI was cons...

Web authoring tools CGI was considered excellent in the beginning since it was also open standard. The only drawback it suffered was that it was slow. Major software developers v

Explain HLL program & execution of machine language program, Give the Schem...

Give the Schematic of Interpretation of HLL program and execution of a machine language program by the CPU. The CPU utilizes a program counter (PC) to notice the address of nex

Why should i use cgi, CGI is significant whenever you require to retain sta...

CGI is significant whenever you require to retain state information about a user, or run an application which communicates with the server. Things like guestbook's, Chat clients, d

Name the popular security measures, Name the popular security measures ...

Name the popular security measures A number of security products covering a broad range of methods are available in the market. Most popular of all the security measures are th

Explain yet another compiler-compiler, Explain Yet another Compiler-Compile...

Explain Yet another Compiler-Compiler. YACC uses for "Yet another Compiler-Compiler": Computer program input usually has some structure; actually, all computer programs which

Basic working of network layer, Q. Basic working of Network layer? Net...

Q. Basic working of Network layer? Network layer: Network layer is responsible for routing a packet within the subnet that is, from source to destination nodes across numerou

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