# Simplifying this equation using Boolean Algerbra

1. Sep 28, 2011

### Ese

1. The problem statement, all variables and given/known data
Where
. or SPACE (" ") = AND
+ = OR
 = NOT (Complementary)

2. Relevant equations
I've been having problems with the second question of my assignment. Here's the equation:
[( a + bc ) + ( b + a'c )]' = F

3. The attempt at a solution
So far, all I've done is this:
[( a + bc ) + ( b + a'c )]'
= [(aa+ac+ba+bc) + (b'b' + b'c + a'b' + a'c)]'
= [a+...

2. Sep 29, 2011

### ehild

Is it [( a + bc ) + ( b' + a'c )]'?

I do not understand what you did. Try to simplify the expression between the square brackets. Do you know the relation a+a'c=a+c? Do you know De Morgan's laws?

ehild

3. Sep 29, 2011

### Ese

I tried this:

= [(aa+ac+ba+bc) + (b'b' + b'c + a'b' + a'c)]'
= [a+...

[( a + bc ) + ( b + a'c )]' = F
= (a+bc)' + (b'+a'c)'
= (a'+(bc)') + (b+(a'c)')
= a.b'c' + b'.ac'
= ab'c' + b'ac'
= ab'c'

Is this correct?

4. Sep 29, 2011

One thing you did wrong was that you forgot to change the symbols for the " ' " equations

ex: (a + b)' = a'b'

So, for your first couple lines:

[( a + bc ) + ( b` + a'c )]'

= (a+ bc)'(b'+ a'c)'
= (a'(bc)')(b(a'c)')
= ............

Last edited: Sep 29, 2011