Logical Expression Simplification.

Question

I'm trying to simply the expression: K = A'B'C' + AB'CD' + B'D' + C'D

These are the steps I got:

K = A'B'C' + ACB'D' + B'D' + C'D (Associative)

K = A'B'C' + B'D' + C'D (Absorption)

I know the answer is K = B'D' + C'D I have been struggling for 2 hours but couldn't find a way to eliminate A'B'C'.

Please advise. Thank you.

Answer 1

A'B'C' = A'B'C'(D'+ D) = A'B'C'D'+ A'B'C'D,
the first of them being covered by B'D' and the second by C'D.

Answer 2

Expand the A'B'C' term. $$K = A'B'C' + AB'CD' + B'D' + C'D$$

$$K = A'B'C' + (AC + 1) B'D' + C'D$$

$$K = A'B'C' + B'D' + C'D$$

$$K = A'B'C'D + A'B'C'D' + B'D' + C'D$$

$$K = ( A'B' + 1 ) C'D + AB'CD' + B'D'$$

$$K = C'D + AB'CD' + B'D'$$

$$K = ( AC + 1 ) B'D' + C'D$$

$$K = B'D' + C'D$$