Boolean Algebra prove

1. Nov 20, 2013

ccky

1. The problem statement, all variables and given/known data

2. Relevant equations

Boolean Algebra

3. The attempt at a solution
I use the distri to change the A+C'.D and Demorgan.
Should i use dis and Demorgan firstly like below?

Which property I should use in the next step?
If the first part is wrong,which property i should use first?
Sorry for the small pictures!
Thanks

2. Nov 20, 2013

Staff: Mentor

Continue to use demorgan until you get down into the simplest form then apply algebra reduction rules.

So are you trying to prove:

(A + C'D)' + A + (CD + AB)' = 1

Just want to make sure we understand the problem as the bar above terms in your images looks like it might include the A term.

Last edited: Nov 20, 2013
3. Nov 21, 2013

ccky

Sorry for the vague picture.The bar not include in the A term.
Should i use the Demorgan in the whole question firstly including the A.
As the picture shows,then,i continue to use Distributive or Absorption,but failed.

4. Nov 21, 2013

Staff: Mentor

In your final expression do you have any terms like this?

X + X' + ...... =?= 1

5. Nov 22, 2013

ccky

I continue to calculate following the picture show on the The attempt at a solution

First:
A'(C+D')+(A+C'+D')(A+A'+B') Use distributive
A'(C+D')+(A+C'+D')(1+B')
But i was wondering whether i can change to 1+B' to 1,because the list only show that 1+A=1

Second:
A'(C+D')+A+A'C'+B'C'+A'D'+B'D'
A'(C+D')+A+A'(C'+D')+B'(C'+D')

6. Nov 22, 2013

Staff: Mentor

It seems you are almost there. The last expression

A'(C+D')+A+A'(C'+D')+B'(C'+D')

can be expanded into

A'C + A'D' + A + A'C' + A'D' + B'C' + B'D'

and then combine some terms to get:

A'(C + C') + A + A'D' + B'C' + B' D'

Do you see how to finish it?

HINT: remember that X' + X = 1 and that 1+ANYTHING = 1 in boolean algebra

7. Nov 22, 2013

ccky

a'+ a + a'd' + b'c' + b' d'
1+a'd' + b'c' + b' d'
1

8. Nov 22, 2013

Staff: Mentor

Thats great!

It floored me too when I got to the second to last step and thought how am I going to reduce that and then I saw the A + A' terms
and realized the other terms just didn't matter.

9. Nov 22, 2013

ccky

Thanks you!!!