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

Show basic concepts of permutation, Q. Show Basic concepts of permutation? ...

Q. Show Basic concepts of permutation? Let us look at the basic concepts of permutation with respect to interconnection network.  Let us say the network has set of n input node

Find traffic offered and lost, Discuss grade of service. During busy hour, ...

Discuss grade of service. During busy hour, 1500 calls were offered to a group of trunks and 8 calls were lost. The average call duration was 120 seconds. Calculate the traffic off

Elucidate basic time division time switching method, With the help of block...

With the help of block diagram Elucidate basic time division time switching method. Basic Time Division Switching: Functional blocks of a memory based time division switching

Vertical alignment of fields one below the other, Which Command permits for...

Which Command permits for vertical alignment of fields one below the other. UNDER Command is used ofr vertical alignment.

Develop a system to store change logs , The ?rst task in the project is to ...

The ?rst task in the project is to develop a sane system to store change logs and versions of ?les. The simplest approach is to create a "dot" directory in the location of the ?le

Database system, What are the three data anomalise that are likely to occur...

What are the three data anomalise that are likely to occur as a result of data redundancy?

What are models and meta models, Model: It is a entire explanation of s...

Model: It is a entire explanation of something (i.e. system). Meta model: It shows the model elements, syntax and semantics of the notation that permits their manipulatio

What is hit and hit rate , What is hit? A successful access to data in ...

What is hit? A successful access to data in cache memory is known as hit. Normal 0 false false false EN-IN X-NONE X-NONE

How do you make an append query, Append query can be used if you would like...

Append query can be used if you would like to add new rows of data to an already active table. The process of making an append query follows these steps they are. ? Basic step

What is rambus dram, Q. What is Rambus DRAM? RDRAM which was developed ...

Q. What is Rambus DRAM? RDRAM which was developed by Rambus has been adopted by Intel for its Pentium and Itanium processors. It has become main competitor to SDRAM. RDRAM chip

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