# Boolean Algebra help

1. Jan 29, 2012

### Tokenfreak

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

I am suppose to use Boolean algebra to show that the following expressions are true.

2. Relevant equations

w'z' + w'xy + wx'z + wxyz = w'z' + xyz + wx'y'z + wyz

3. The attempt at a solution

I have tried to figure out how to get to that answer above but I am stuck and not sure what to do or if I am even doing it right. Here is what I got so far:

w'(z + xy) + w(x'z +xyz)
w'(z + xy) + wz(x' + xy)
w'(z + x' + y') + wz(x' + x' + y')
w'(z + x' + y') + wz(x' + y')

Thanks!

2. Jan 31, 2012

### Staff: Mentor

When a solution is not obvious, consider whether to first draw up truth tables to show that equality holds. If there is an error in the expressions you are given, this will reveal it before you waste a lot of time on an exercise in futility.

3. Jan 31, 2012

### Joffan

You have some errors in your derivation; xy ≠ x'+y' , for example.

Here's a hint: w'xy = w'xy(z+z') = w'xyz + w'xyz'

And yes, truth tables are definitely useful here.

4. Jan 31, 2012

### Dzung

Y=(AB)+(~AC)+(BC)

Z= (AB)+(~AC)

thanks

5. Jan 31, 2012

### Joffan

Help #1: Use truth tables
Help #2: BC = (A+~A)BC