# Simplifying Boolean Expression AB'C⋅(BD+CDE)+AC'

I'm currently stuck on the expression listed below. I applied almost all the Boolean algebra rules trying to figure it out, but no luck

Here is the expression $$\boxed{\mathtt{AB'C\cdot(BD+CDE)+AC'}}$$

• Applying Distributive law
AB'CBD + AB'CCDE + AC'

• Applying A⋅A'=0 and C⋅C=C
AB'CDE+AC'

• Factoring
A⋅(B'CDE+C')

This is where I'm stuck. This is where I tried most of the rules and got nowhere

The Textbook Solution however is: $$\boxed{\mathtt{A⋅(C'+B'DE)}}$$

Then, I found this site and it also gave me a different solution. Their solution was $$\boxed{\mathtt{A \cdot C'}}$$

I don't know if the book has a wrong solution, or an alternate one.

Any suggestions? Thanks.

• Your book's answer is right. The web site you linked doesn't like "E". (Just look at the table they generate -- it is missing a column for E.) So just replace "E" with "F" on that web site and see what answer it gives you then. Note that it generates a proper table, too, if you use F instead of E.
– jonk
Sep 20, 2018 at 4:30