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 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

Determine the types of software, Determine the types of software There ...

Determine the types of software There are two types of software today: Application and systems. Meaning of the two changes computer to computer. As we concentrate on large c

The periodic table of elements, Make a data structure to store information ...

Make a data structure to store information about the elements in the periodic table of elements.  For each element, store the name, atomic number, chemical symbol, class, atomic we

What is neg instruction, What is NEG instruction Arithmetic sign inver...

What is NEG instruction Arithmetic sign inversion or two's complement (NEG). NEG instruction two's complements a number which means that arithmetic sign of a signed number cha

Approach to reasoning - first-order logic, Approach to reasoning - first-or...

Approach to reasoning - first-order logic: The formal approach to reasoning has bigger return and disadvantages. In generally we notice, if a computer program has proved somet

Illustrate working of magnetic bubble memories, Q. Illustrate working of Ma...

Q. Illustrate working of Magnetic Bubble Memories? In many materials like garnets on applying magnetic fields certain cylindrical areas whose direction of magnetization is oppo

Analog to digital convertor, In which A/D converter has the speed of conver...

In which A/D converter has the speed of conversion is maximum ? Ans. In Parallel-comparator A/D converter, the speed of conversion is maximum. Speed of conversion is maximum a

Explain crossbar exchange with all call processing steps, Explain crossbar ...

Explain crossbar exchange, with all call processing steps and diagrams. The fundamental idea of crossbar switching is to give a matrix of n x m sets of contacts with only n + m

Determine the minimum bandwidth of the system, Data is to be transmitted us...

Data is to be transmitted using a modem at 9600 bps. Determine the minimum bandwidth of the system with the following modulation methods (a) FSK (b) ASK. Use the excess bandwidth f

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