De morgan''s laws - artificial intelligence, Computer Engineering

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.

Posted Date: 10/2/2012 8:04:29 AM | Location : United States







Related Discussions:- De morgan''s laws - artificial intelligence, Assignment Help, Ask Question on De morgan''s laws - artificial intelligence, Get Answer, Expert's Help, De morgan''s laws - artificial intelligence Discussions

Write discussion on De morgan''s laws - artificial intelligence
Your posts are moderated
Related Questions
Aim: Build a program or application which gives an interface to the user to maintain his personal account for E-mails & should be able to work on the following applications. Des

"Super ASCII", if it contains the character frequency equal to their ascii values. String will contain only lower case alphabets (''a''-''z'') and the ascii values will starts from


Q. Differentiate the Multiplexer and Demultiplexer with respect to their concept, block diagram and circuit. Q. What is the difference between Synchronous sequential circuits an

It is helped to recure the bugs. A program has problem that time this debugging is helped to solve the bugs is simply, this is the method of the recure bugs in the programming lang

Q. How to use an Assembler? Symbolic instructions which we code in assembly language is called as- Source program. An assembler program translates source program in machine

The expansion of nested macro calls done by using of? Ans. LIFO rule is used for the expansion of nested macro calls.

When we initialize the form at that time if we require to set any variable's value then we can set it by defining in constructor. Constructor's name always similar as class name an

How to select valid lines for secondary list? To stop the user from selecting invalid lines, ABAP/4 offers various possibilities.  At the end of the processing block END-OF-SEL

Basic elements of  Assembly language: Any Assembly language which consists 3 types of instruction statements that are used to define the program operations: Data secti