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## Homework Statement

Simplify the expression using boolean algebra postulates, laws, theorems.

[itex](\overline{\overline{x + \overline{y})(xz + \overline{y}}) + x (\overline{yz}})[/itex]

## The Attempt at a Solution

[itex](\overline{\overline{x + \overline{y})(xz + \overline{y}}) + x (\overline{yz}})[/itex]

1. ((x + y')(xz + y'))'' (x(yz)')'

2. (x + y')(xz + y') (x' + (yz)'')

3. (x + y')(xz + y') (x' + yz)

4. (x + y')(x + y')(z + y')(x' + yz)

5. (x + y')(z + y')(x' + yz)

6. (xz + y')(x' + yz)

7. xzx' + xzyz + y'x' + y'yz

8. xx'z + xyzz + x'y' + y'yz

9. 0*z + xyz + x'y' + 0*z

10. 0 + xyz + x'y' + 0

11. xyz + x'y'

Am I on the right track? I keep thinking that I've done something wrong here... Thanks in advance for your help.

Edit: Added steps 4-11. I believe this is the most simplified. Any critique on my methods? Perhaps there is a more efficient way to simplify this? Thanks.

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