# Help needed with Boolean Algebra and DeMorgan

#### randb

Joined Dec 29, 2012
16
Demorgan problem

(( AB') (A'C))' One broke bar recd (AB')' + (A'C)'

then broke the bar again and recd A'+B+A+C' A'+a =1 1+ other variables =1?

Book states answer is (A+B') ( A'+C)

Where did I go wrong?

#### R!f@@

Joined Apr 2, 2009
9,751
What's wrong with your title ?

#### amilton542

Joined Nov 13, 2010
497
Why are you applying boolean operators to expressions alone?

#### jjw

Joined Dec 24, 2013
720
The answer in the book is wrong if the original expression is correct.

#### amilton542

Joined Nov 13, 2010
497
$$Y = [(AB')(A'C)]'$$

$$Y = (AB')' + (A'C)'$$

$$Y = (A'+B)(A+C')$$

Which is the same as you've got.

You're operating on expressions alone though, which is O.K, but could you type this "question" in it's entirety because something's missing.

Last edited:

#### jjw

Joined Dec 24, 2013
720
$$Y = [(AB')(A'C)]'$$

$$Y = (AB')' + (A'C)'$$

$$Y = (A'+B)(A+C')$$

Which is the same as you've got.

You're operating on expressions alone though, which is O.K, but could you type this "question" in it's entirety because something's missing.
Last expression is missing + should be (A'+B)+(A+C')

#### randb

Joined Dec 29, 2012
16
Applying DeMorgan's theorem and Boolean algebra to the expression
results in _____.

#### randb

Joined Dec 29, 2012
16
Thank you for your responses and help

#### amilton542

Joined Nov 13, 2010
497
Last expression is missing + should be (A'+B)+(A+C')
Oops, yes you're right. I missed that one somehow.

In all fairness, I really don't know. Maybe someone else could help you.

#### WBahn

Joined Mar 31, 2012
26,398
Demorgan problem

(( AB') (A'C))' One broke bar recd (AB')' + (A'C)'

then broke the bar again and recd A'+B+A+C' A'+a =1 1+ other variables =1?

Book states answer is (A+B') ( A'+C)

Where did I go wrong?
Did you go wrong?

Let's check it out. You are claiming that the expression

((AB') (A'C))' = 1

This is of the form

(FG)' = 1

which is

FG = 0

F = AB'
G = A'C

If A is False, then F is False and FG is False.
If A' is False, the G is False and FG is False.

What does that tell you?