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

What is reduction, What is reduction?  A reduction is a way of changing...

What is reduction?  A reduction is a way of changing one problem into another in such a way that a solution to the second problem can be used to explain the first problem.

Seven segment decoder, A design for the seven segment decoder is required. ...

A design for the seven segment decoder is required. The decoder has four inputs which represent a number from 0 to 9 in binary and seven outputs which are connected to the seven

Explain the do while loops, Explain The do while loops The do while loo...

Explain The do while loops The do while loops is similar, but the test occurs after the loop body is executed. This ensures that the loop body is run at least once.

Describe ergonomic keyboards, Q. Describe Ergonomic Keyboards? Ergonomi...

Q. Describe Ergonomic Keyboards? Ergonomics is the study of environment, conditions as well as efficiency of workers. Ergonomics proposes that keyboard wasn't designed with hum

State the important features of operating system, a. Define operating syste...

a. Define operating system? State the important features of operating system? b. Describe the following facilities for implementing interacting processes in programming language

Grapgh, representation of the adjacency matrix and adjacency list

representation of the adjacency matrix and adjacency list

Flat, nfa significance

nfa significance

What are the elements of analysis model, What are the elements of Analysis ...

What are the elements of Analysis model? i. Data Dictionary ii. Entity Relationship Diagram iii. Data Flow Diagram iv. State Transition Diagram v. Control Specifica

Explain the boolean equations for logic circuits, Explain The Boolean Equat...

Explain The Boolean Equations for Logic Circuits? A Boolean equation is the mathematical representation of a logic circuit using standard Boolean terms. All the logic gates (AND,

What is the working of sound cards, Q. What is the working of Sound cards? ...

Q. What is the working of Sound cards? Multimedia has become a very significant part of today's PC. Home user wants hear songs and watch movies. The Software developer hacking

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