boolean algebra x=A.B.C+A'C

I have a question on Boolean algebra

I have to simplify the following expressions-

(1) x = ABC+A'C (where A'=notA)

= BC(A+A')

= BC(1)

= BC

(2) q = R'S'T'(R'+S'+T')

= R'R'S'T'+S'R'S'T'+T'R'S'T'

= R'S'T+R'S'T'+R'S'T'

= R'S'T'

(3) z = (B+C')(B'+C)+A"+B'+C"

(4) y = (C'+D')+A'CD'+A'B'C'+A'B"CD+ACD'

Im new to the Boolean algebra and want to know if the first two questions(1&3) are correct.

and if possible,i need some help simplifying the last two question(3&4) I have no idea were to start

Thanks

• Regarding simplification, if this is school homework (and you need to "show your work"), you should probably read up on Karnaugh map. Otherwise use Espresso or some front end for it like Logic Friday. Even Wolfram Alpha can simplify Boolean expressions, but you need to use a different syntax. – Fizz Feb 11 '15 at 16:14
• In some of the expressions you have a double quote " instead of single quote '. Are you having a double negation, or is it a typo? – Roger C. Mar 14 '15 at 9:50
• On equation 1, you are trying to factor BC out of both sides of the +. If the equation was ABC + A'BC you could do that, but that's not what you are starting out with. – tcrosley Mar 14 '15 at 10:27
• Do you still need help? – Daniel Tork Apr 18 '17 at 5:59

ABC + A'C

C (AB + A')

C (B + A') or BC + A'C

1. is correct.

2. Assuming '' is legitimate.

A'' = NOT NOT A = A First two terms are an XOR. Multiply them out.

Then look for common terms and minimize.

Here's a link to boolean rules. Try and repost.

1) Wrong. $ABC+A'C\ne BC(A+A')$
2) On the second line of the solution you have a missing ' on first term, but the final is correct.
(3&4) Try to figure it out. Start with double NOTs, of course, and looking for familiar patterns.

You can easily check your answers by comparing the truth tables of the left and right sides.