Solve Boolean Algebra Homework Problem

[Tokenfreak]

Homework Statement

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

Homework Equations

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

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!

 

[NascentOxygen]

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.

 

[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.

 

[Dzung]

can someone please help simplify the below two Boolean Algebra expressions.

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

Z= (AB)+(~AC)

thanks

 

[Joffan]

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