Hello, I had to do complete the problems as outlined below this paragraph. I completed parts a-b as per the attached image, however I cannot complete part c which is 'how to use De Morgan's theorem to prove a relationship between the two Karnaugh map simplified formulas'. Can anyone see what I am doing wrong here ?
Thanks kindly for any help.

(a)
Design a circuit which has the four bits of a BCD number as its inputs and
has an output X so that:
X = 0 if inputs are a valid BCD number
X = 1 if inputs are an invalid BCD number.
(b)
Redesign the circuit of (a) so that:
X = 1 for valid BCD
X = 0 for invalid BCD.
(Note: DO NOT just invert your input (a).)
(c)
Use de Morgan’s theorem to prove that the Boolean Algebra expressions
you obtained in (a) and (b) are the inverse of each other.

 

How can we tell what you are doing wrong on Part C when you haven't shown us what you are doing on Part C at all?

Your Part A and Part B work is fine.

Post your best effort for Part C so that we have a springboard to work from.

 

Hint!

Rewrite your solutions in parts a and b, to use different variables:

X=A(B+C)
Y=A'+B'C'

Then, to prove part C, you need to show that X and Y' are the same. Using DeMorgan's, this is easy...