1. ## DeMorgan's law help

I have this:

X = ABC + BCD

(BCD has a not line over it)

X = ABCD

(X and A have a not line over them)

Can someone show me the steps to get to the answer?

2. Hello,

$\bar X=(\overline{ABC})(BCD)=(\bar A+\bar B+\bar C)(BCD)$ $=\bar A BCD+\bar B BCD+\bar C BCD=\bar A BCD+(\bar B B)CD+(\bar C C)BD$

Recall that for any P, $\bar P P=0$, that + and * are associative, etc...

3. Thanks. I have one more quick question regarding DeMorgan's law.

Say I have
$\overline{\bar B+\bar C+AD}$

Does it become:
$BC \overline{AD}$

Then:
$(\bar A+\bar D)BC$

4. Yes and yes