SOP expression simplify I wanted to know how to simply this SOP expression using Boolean Algebra :
F= A'BC'+A'BC+ABC
I got this answer using K - Map: (A'B+BC), but I want to know how do get it using Boolean Algebra Rules.
Thank you.
 A: You can relate the Boolean Algebra manipulations directly to what you do in a K-map.
Consider the K-map for this expression:

Now, note that the red oval represents the expression $A'B$ while the blue oval represents $BC$. Moreover, the red oval covers the terms $A'BC$ and $A'BC'$, while the blue oval covers the terms $ABC$ and $A'BC$.
So, we have that $A'B = A'BC + A'BC'$ and $BC=ABC+A'BC$, which are both instances of the general Adjacency principle:
Adjacency
$P = PQ + PQ'$
Indeed, note that Adjacency is named exactly after the fact that you combine two adjacent terms in a K-Map into one.
OK, so we thus have that:
$A'BC+A'BC'+ABC+A'BC \overset{Adjacency \ x \ 2}= A'B+BC$$
Hmmm ... that is almost your starting expression $A'BC'+A'BC+ABC$, except there are two  $A'BC$ terms instead of one.  However, we can get that second one easily enough:
Idfempotence
$P = P + P$
OK, so we are now ready to apply the Boolean algebra on your original expression:
$A'BC'+A'BC+ABC \overset{Idempotence}= A'BC'+A'BC+A'BC+ABC \overset{Adjacency \ x \ 2}= A'B+BC$$
A: 
I hope this is more easy for begginers !
