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

Explain about disk caching scheme, Q. Explain about disk caching scheme? ...

Q. Explain about disk caching scheme? The disk caching scheme can be used to speed up performance of disk drive system. A set (cache) of buffers is assigned to hold some disk b

Show the decimal equivalent of a binary number, Q. Show the Decimal equival...

Q. Show the Decimal equivalent of a binary number? In binary numbers we have two digits 0 and 1 in addition they can also be signified as a string of these two-digits known as

How to create a layout table in dreamweaver, Q. How to Create a Layout Tabl...

Q. How to Create a Layout Table in dreamweaver? In last section you used cells to create a table. Now, you will see how to start with a table and add cells later. 1.  In Obj

What is external procedures, Q. What is External Procedures? These proc...

Q. What is External Procedures? These procedures are written as well as assembled in separate assembly modules and afterwards linked together with the main program to form a bi

What is the working of domain expert, Q. What is the working of domain expe...

Q. What is the working of domain expert? ANSWER: The domain expert is the person who gives the domain expertise in the form of problem-solving strategies.

What is icon, An icon is a picture used to show an object. Some example obj...

An icon is a picture used to show an object. Some example objects are: data files, program files, folders, email messages, and drives. Every type of object has a dissimilar icon. T

Design a 1-bit full adder, Design a 1-bit full adder: Verify your desig...

Design a 1-bit full adder: Verify your design Use the 1-bit full adder to build a 4-bit adder with Ci=0 Verify: 1 + 4, and 9 + 9 Sram design: Cell: p - 0.5/0.045;

Name the abap/4 modularization techniques, Name the ABAP/4 Modularization t...

Name the ABAP/4 Modularization techniques. Techniques are:- Source code module. Subroutines. Functions.

What is selective complement - logic micro operations, SELECTIVE COMPLEMEN...

SELECTIVE COMPLEMENT The selective-complement process complements bits in register A where there are corresponding 1's inside register B. It does not affect bit positions which

What are the rules of timescale directive, What are the Rules of Timescale ...

What are the Rules of Timescale directive Rules -  'Timescale directive, like all compiler directives, affects all modules compiled after directive,  whether  in  same  fi

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