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
Syntax and Semanticsx and Semantics for First-order logic - artificial intelligence: Propositional logic is limited  in its expressiveness: it may just represent true and false

Q. Instruction set for IA - 64 architecture? Instruction set: Architecture gives instructions for multimedia operations as well as floating point operations. Itanium supports

Q. What is Parallel Loop Construct? Parallel loop construct is a shortcut for specifying parallel construct comprising one loop construct and no other statements. The syntax of

failed logins to end

All SAP Databases are Relational Databases is the all sap databases.

Problem : a) What do you meant by a Multimedia Authoring System? b) Compare the verbose syntax to the dot syntax in Lingo. c) Explain each of the following terms: i) L

Q. Explain about Layout Cells? In Layout view you can draw layout cells and layout tables to define design areas of a document. This task is easier to accomplish if you prepare

A communication protocol is an agreement which specifies a common language two computers use to exchange messages. For instance, a protocol specifies exact format and meaning of ev

Scenarios encapsulate the Vuser Groups and scripts to be implemented on load generators at run-time. Manual scenarios can deal out the total number of Vusers between scripts bas

Q. Show Organisation of Clos network? Clos network: This network was designed by Clos (1953).  It's a non-blocking network and offers full connectivity similar to crossbar netw