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

Define class p, Define class P  The class of all sets L that can be kno...

Define class P  The class of all sets L that can be known in polynomial time by deterministic TM. The class of all decision problems that can be decided in polynomial time.

Why cmos circuits are extensively used for On-chip computers, CMOS circuits...

CMOS circuits are extensively used for ON-chip computers mainly because of their extremely ? Ans. Since CMOS circuits have large packing density, so these are extensively use

Microprocessors and motherboards, Module Learning Outcomes for This Assignm...

Module Learning Outcomes for This Assignment 1. Design and minimize a digital electronic circuit using logic devices from ttl and cmos. 2. Explain the hardware design of

What do you mean by file, Q. What do you mean by File? In computer voca...

Q. What do you mean by File? In computer vocabulary, file is a collection of text or data stored on a storage device, such as a Floppy Disk or Hard Disk. If you a fresher to c

Determine the complete or gate and and gate decoder, Q. Determine the comp...

Q. Determine the complete OR gate and AND gate decoder count for an IC memory with 4096 words of 1 bit each, using the Linear select memory organization and Two dimensional Memory

Explain the term - rational rose and visio 2000 enterprise, Explain the ter...

Explain the term - Rational Rose and Visio 2000 Enterprise Rational Rose: IBM Rational RequisitePro is a powerful and easy-to-use tool for use case management and requirement

Applications of electronic data interchange in business, What are the appli...

What are the applications of Electronic Data Interchange in business? The applications of Electronic Data Interchange are as given below: 1. Organisations that use EDI 2

Input-output-processor interconnection network (iopin), Input-Output-Proces...

Input-Output-Processor Interconnection Network (IOPIN): This interconnection network is designed for communication between I/O Channels and processors. Every single one proces

C programming, A palindrome is a string that reads the same from both the e...

A palindrome is a string that reads the same from both the ends. Given a string S convert it to a palindrome by doing character replacement. Your task is to convert S to palindrome

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