How do you simply the following equation?
$$X = A'B'C'D' + A'B'CD' + A'BCD' + ABCD' + AB'CD'$$
Here is what I did:
$$\begin{eqnarray}
X & = & A'B'C'D'+A'CD'(B'+B) + ACD'(B+B') \\
& =& A'B'C'D'+CD'(A'+A) \\
& = & D'(A'B'C'+C)
\end{eqnarray}$$
Is this correct?
Best Answer
It looks great. The one improvement that could be made is that the $C'$ is redundant, owing to an identity:
$$ZY'+Y=Z+Y$$
You can deduce this using the absorbtion law $ZY+Y=Y$, and the complementary law $Y+Y'=1$.
Intuitively, when adding part of $Z$ outside of $C$ to $C$, you may as well add all of $Z$ to $C$, because the part already inside $C$ will be abosorbed anyway.