Complement vs. dual?

Question

Is COMPLEMENT OF DUAL=DUAL OF COMPLEMENT?

How can we relate in terms of minterms,

like if f(x,y,z)=0,1,2,3,
then complement = 4,5,6,7

 

what would be the dual?

Comments

then dual is max terms of  0,1,2,3

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max terms is total-minterms right?

which would be same as complement? isnt it?

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yeap

Answer 1

yes!

COMPLEMENT OF DUAL=DUAL OF COMPLEMENT

Complement of dual

we have function,$F(w,x,y,z,+,.,0,1)$

dual of it, $F_D(w,x,y,z,.,+,0,1)$

complement of it,$[F_D(w,x,y,z,.,+,0,1)]' =F_N(w',x',y',z',+,.,1,0)$

Dual of complement 

we have function,$F(w,x,y,z,+,.,0,1)$

complement of it, $[F(w,x,y,z,+,.,0,1)]' =F_C(w',x',y',z',.,+,1,0)$

dual of it,$F_N(w',x',y',z',+,.,1,0)$

Example:

consider a + b' .
i)( COMPLEMENT OF DUAL)its dual is ab'. now the complement is (ab')'=a'+b
ii)(DUAL OF COMPLEMENT)its complement is a'b. dual would be a'+b.
 

Comments

your can disprove but not prove by giving 1 exmaple.

Answer 2

dual means for example:

dual of ABC=A+B+C

A.o=A+1

Answer 3

COMPLEMENT OF DUAL=DUAL OF COMPLEMENT  its correct .

Lets take example -> 

f(x,y,z)=$\sum$m ( 0,1,2,3 )

1.  COMPLEMENT OF DUAL

fd (dual of f) = $\prod$M ( 7, 6, 5, 4 )

fd' =   $\sum$m ( 7, 6, 5, 4 )       

2.  DUAL OF COMPLEMENT

f'=$\prod$M ( 0,1,2,3 )

f'd =   $\sum$m ( 7, 6, 5, 4 )   =  fd'