# Boolean algebra

• 04-01-2010
akansha
Boolean algebra

Explain concept of “DUALITY” with example.
[ eg: solve this (a . b . c . d’ . e)’ ]
• 04-01-2010
claudiu
You can find help on this great site:

Let me topeka that for you

It never gets old. ;)
• 04-01-2010
rob90
Quote:

Originally Posted by akansha

Explain concept of “DUALITY” with example.
[ eg: solve this (a . b . c . d’ . e)’ ]

I think that (a . b . c . d . e) should become (e . d . c . b. a) in fact it's just the opposite of the original order relation and it is a duality because it is a "transformation of the structure in itself in which you can find part of the notions related to it", (from my book of logic) in this case they are both order relations but the first is an ascending order <, while the second is descending >
• 04-02-2010
zalezog
Quote:

Originally Posted by akansha

Explain concept of “DUALITY” with example.
[ eg: solve this (a . b . c . d’ . e)’ ]

Given a Boolean expression, its dual is formed by replacing '+' with '.' , '.' with '+', 0 with 1 or 1 with 0.

Given a boolean equation like x + 1 = 1, its dual is x . 0 = 0 and when you prove x + 1 = 1,
its dual follows 'By the Principle of Duality' and you don't need to prove x . 0 = 0

I think what you are looking for is the DeMorgan's Law where
(a . b . c . d’ . e)’ = a' + b' + c' + d + e'

But then i really don't know how do you "explain the concept of duality with an 'expression'."
• 04-02-2010
akansha
Quote:

Originally Posted by zalezog
Given a Boolean expression, its dual is formed by replacing '+' with '.' , '.' with '+', 0 with 1 or 1 with 0.

Given a boolean equation like x + 1 = 1, its dual is x . 0 = 0 and when you prove x + 1 = 1,
its dual follows 'By the Principle of Duality' and you don't need to prove x . 0 = 0

I think what you are looking for is the DeMorgan's Law where
(a . b . c . d’ . e)’ = a' + b' + c' + d + e'

But then i really don't know how do you "explain the concept of duality with an 'expression'."

The concept that you have explained is called "compliment". "Duality" is a different concept.
The definition of Duality is "Duality says that one part may be obtained from other if binary operators and identity elements are interchanged."
I hope this could help.

Regards
Akansha
• 04-02-2010
cyberfish
• 04-03-2010
zalezog
Quote:

Originally Posted by akansha
The concept that you have explained is called "compliment". "Duality" is a different concept.
The definition of Duality is "Duality says that one part may be obtained from other if binary operators and identity elements are interchanged."

and i said
Quote:

Given a Boolean expression, its dual is formed by replacing '+' with '.' , '.' with '+', 0 with 1 or 1 with 0.

Quote:

Originally Posted by akansha
I hope this could help.

?