Sum of Product and Product of Sum

Question

I have a doubt it may be stupid though.

know that if ∑m (1,3,5,6) then its equivalent  POS form is =  πM (0,2,4,7)

But my doubt is say i need to represent  7, in SOP i write ABC in POS i write (A'+B'+C')
∑m (1,3,5,6) = A'B'C + A'BC+AB'C+ABC'

if i take complement of it = Duality + complement every literal then it becomes :

(A+B+C')(A+B'+C')(A'+B+C')(A'+B'+C) = πM(1,3,5,6)

then why we say that SOP is complement of POS and why ∑m (1,3,5,6) != πM(1,3,5,6) ? as according to above they seems to be equal.

Comments

what i want to say is..they are not complement ..

say if fun is 1 at value 0,1,3 then definately at remaining values of input it has 0 value ...

Answer 1

SOP and POS are not complement of each other ...

They are just a way to represent the Values where function have value 1 or 0 as in digital logic we have either 0 or 1 ..have a look at this ...its NPTL refrence

Comments

Some Doubts:-

1.

So brother then  ∑m (1,3,5,6) =  πM (0,2,4,7) what is this ?

Isn't it the complement of the function.

Ok i guess if say For example a Bulb which glows at the input 1 or 3 or 5 or 6 so its complement should be that it should not glow on these points but rather on the other points which are 0 or 2 or 4 or 7.

2.

If i want to represent the complement of the function given by  ∑m (1,3,5,6) in SOP only not in POS what would it be ?

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Brother please help me here :)

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For example a Bulb which glows at the input 1 or 3 or 5 or 6

 Bulb glows at the input 1 or 3 or 5 or 6 ( treat them as Minterms ) = ∑m(1,3,5,6)

it means Bulb doesn't glows at the input 0 or 2 or 4 or 7  ( Both are equal ) = ∏ (0,2,4,7)

 

it's complement is

Bulb doesn't glows at the input 1 or 3 or 5 or 6 = ∏(1,3,5,6) = ∑(0,2,4,7)

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For avoiding confusion, let take F(A,B) = AB

F = AB = ∑(3) = ∏(0,1,2)

what is F' ?

F' = (AB)' = A' + B' = A'B' + A'B + AB' + A'B' = A'B' + A'B + AB' = ∑(0,1,2) = ∏(3)

 

if you have f = ∑( k terms ) then

( total - k terms ) -------> if you keep them as Maxterms, then it is same function.

                         -------> if you keep them as Minterms, then it is complement of the function.

 

Note that, Complement of POS form is SOP form ( converse also true )

But it didn't means Complement of function is interchanging the SOP and POS forms.