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

Search mechanisms in prolog - artificial intelligence, Search mechanisms in...

Search mechanisms in Prolog We can utilize this simple Prolog program to describe how Prolog searches: president(X) :- first_name(X, georgedubya), second_name(X, bush). p

Structure of 8086 cpu, 8086 microprocessor comprises two independent units:...

8086 microprocessor comprises two independent units:  1.  Bus Interface unit 2.  Execution unit Please refer to Figure below. Figure: The CPU of INTEL 8086 Microp

Electrical technology, voltage,current and power relation in a delta connec...

voltage,current and power relation in a delta connection

What are micrographics, What are micrographics? A micrographic is an im...

What are micrographics? A micrographic is an image or photographic reproduction of an object which is then changed to film. Micrographics are frequently used for permanent reco

Classification based on grain size, Classification Based On Grain Size ...

Classification Based On Grain Size  This classification is based on identifying  the parallelism in a program to be implemented on a multiprocessor system. The plan is to recog

A luminous jewel game, a luminous jewel game c programming start with t and...

a luminous jewel game c programming start with t and end with t the output will yes or no

What do you mean by internet, Q. What do you mean by Internet? Ans: In...

Q. What do you mean by Internet? Ans: Internet is a network of networks or collection of networks. Several networks such as WAN and LAN connected through suitable hardware an

What is replacement policy in cache, Q.What is Replacement Policy in cache?...

Q.What is Replacement Policy in cache? When a new block has to be fetched in cache the other block may have to be replaced to make room for new block. Replacement policy determ

ANS, Smugglers are becoming very smart day by day. Now they have developed ...

Smugglers are becoming very smart day by day. Now they have developed a new technique of sending their messages from one smuggler to another. In their new technology, they are send

Give explanation of user datagram protocol, Explain UDP (User Datagram Prot...

Explain UDP (User Datagram Protocol). UDP utilizes a connectionless communication paradigm. It is an application of using UDP doesn't require preestablishing a connection befor

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