Find the complement and dual of F=[1+(A+B\')A+D\'E\'][F\'+GH\'(A+0)]+C Do not si

Question

Find the complement and dual of
F=[1+(A+B')A+D'E'][F'+GH'(A+0)]+C
Do not simplify.
I got an answer of F'=[F(G'+H+A')]C' for complement. Couldsomebody please verify? I'm not very confident with myanswer.
Also, I'm having trouble with the dual.
Will rate life saver! Thanks.
F=[1+(A+B')A+D'E'][F'+GH'(A+0)]+C
Do not simplify.
I got an answer of F'=[F(G'+H+A')]C' for complement. Couldsomebody please verify? I'm not very confident with myanswer.
Also, I'm having trouble with the dual.
Will rate life saver! Thanks.

Explanation / Answer

Gvien F= [1+(A+B')A+D'E'] [F'+GH'(A+0)] + C Complement of it will be F ' ={ [1+(A+B')A+D'E'][F'+GH'(A+0)]+C }' F' = { [1+(A+B')A+D'E'][F'+GH'(A+0)] } 'C ' F' = { [1+(A+B')A+D'E']' + [F'+GH'(A+0)]' }C ' F' = { [1' [(A+B')A]' [D'E']' + F [GH'(A+0)]' }C ' F' = { [0 [(A+B')A]' [D'E']' + F [G'+H' + (A+0)'] }C ' F' = F [ G' + H' + A' ] C' To find the dual fucntion, replace 0's by 1's , 1's by0's , product by sum and sum byproduct F= [1+(A+B')A+D'E'] [F'+GH'(A+0)] + C Fd = {[ 0. (A.B')+A (D'+E') ] + [F' (G+H') +A] } C Fd = {A(D' + E' ) + [F' (G+H') + A] } C F' = { [1+(A+B')A+D'E']' + [F'+GH'(A+0)]' }C ' F' = { [1' [(A+B')A]' [D'E']' + F [GH'(A+0)]' }C ' F' = { [0 [(A+B')A]' [D'E']' + F [G'+H' + (A+0)'] }C ' F' = F [ G' + H' + A' ] C' To find the dual fucntion, replace 0's by 1's , 1's by0's , product by sum and sum byproduct F= [1+(A+B')A+D'E'] [F'+GH'(A+0)] + C F' = { [1' [(A+B')A]' [D'E']' + F [GH'(A+0)]' }C ' F' = { [0 [(A+B')A]' [D'E']' + F [G'+H' + (A+0)'] }C ' F' = F [ G' + H' + A' ] C' To find the dual fucntion, replace 0's by 1's , 1's by0's , product by sum and sum byproduct F' = { [0 [(A+B')A]' [D'E']' + F [G'+H' + (A+0)'] }C ' F' = F [ G' + H' + A' ] C' To find the dual fucntion, replace 0's by 1's , 1's by0's , product by sum and sum byproduct F' = F [ G' + H' + A' ] C' To find the dual fucntion, replace 0's by 1's , 1's by0's , product by sum and sum byproduct F= [1+(A+B')A+D'E'] [F'+GH'(A+0)] + C Fd = {[ 0. (A.B')+A (D'+E') ] + [F' (G+H') +A] } C Fd = {A(D' + E' ) + [F' (G+H') + A] } C

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