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

Determine about the radio frequency, Determine about the Radio Frequency (R...

Determine about the Radio Frequency (RFID)  This method includes using small electronic devices containing an Identification microchip and antenna; they work in a similar way

What is edi (electronic data interchange), What is EDI (Electronic Data Int...

What is EDI (Electronic Data Interchange)? EDI: Electronic Data Interchange (EDI) is used by organizations for transactions that happen on regular basis to a pre-determined for

Name the appliances which are controlled by micro-processor, Name the appli...

Name the appliances which are controlled by micro-processor Many household appliances which are microprocessor-controlled do not have operating systems (for example microwave o

Handling multiple devices - computer architecture, Handling Multiple Device...

Handling Multiple Devices Interrupt Priority   Continue to accept interrupt requests from higher priority components   Disable interrupts from component at the sa

Example on passing parameters through stack, Q. Example on Passing Paramete...

Q. Example on Passing Parameters through Stack? PROGRAM: Version 3 DATA_SEG               SEGMENT                         BCD DB 25h; Storage for BCD test value BIN

Decision table, Write a decision table that specifies the rules for the gam...

Write a decision table that specifies the rules for the game of checkers

Define synchronous bus, Define synchronous bus. Synchronous buses are t...

Define synchronous bus. Synchronous buses are the ones in which every item is transferred during a time slot(clock cycle) known to both the source and destination units. Synchr

What is test factory, Rational Test Factory is a component-based testing to...

Rational Test Factory is a component-based testing tool that automatically produces TestFactory scripts according to the application's navigational structure. TestFactory is integr

Operation of micro-programmed control unit, Micro-instructions are stored i...

Micro-instructions are stored in control memory. Address register for control memory comprises the address of subsequent instruction which is to be read. Control memory Buffer Regi

Discuss briefly subscriber loop system, Discuss briefly subscriber loop sys...

Discuss briefly subscriber loop system. Subscriber Loop System: Every subscriber in a telephone network is connected usually to the nearest switching office using a dedicated

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