How to Correctly Simplify This Boolean Expression?

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SUMMARY

The discussion focuses on simplifying the Boolean expression xyz + x'(w + z') + yz(w + z'). The user attempts to simplify the expression and arrives at xyz + x'w + x'z' + yzw, while the textbook states the simplified form is xyz + x'w + x'z'. The confusion arises from the presence of the term yzw, which the user believes cannot be eliminated. The solution provided suggests using the identity yzw = yzw(x + x') to facilitate further simplification.

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Homework Statement


Simplify the following
xyz + x'(w+z') + yz(w+z')


Homework Equations





The Attempt at a Solution


xyz + x'(w + z') + yz(w + z')
xyz + x'w + x'z' + yz(w + z')
xyz + x'w + x'z' + yzw + yzz'
xyz + x'w + x'z' + yzw + 0

I got the answer xyz + x'w + x'z' + yzw

However in the book it says the answer is xyz + x'w + x'z'. How could that be? I don't see any way of getting rid of yzw. Please tell me if this is correct or I need to fix something. Thank you.
 
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If y=z=w=1, just the first three terms will evaluate to 1, regardless of what x equals, so yzw is apparently hidden in there.

Use xyz + x'w + x'z' + yzw = xyz + x'w + x'z' + yzw(x+x'). Multiply the last term out and then simplify.
 

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