Please use algebraic manipulation to prove the following statement: x'y'z' + x'yz' + x'yz + xyz'...
Please use algebraic manipulation to prove the following statement:
x'y'z' + x'yz' + x'yz + xyz' = x'z' + x'y + yz'
Homework Answers
x'y'z' + x'yz' + x'yz + xyz' = x'y'z' + (x'yz' + x'yz') + x'yz + xyz' (since x'yz' + x'yz' = x'yz', because a+a = a) = x'y'z' + (x'yz' + x'yz' + x'yz') + x'yz + xyz' (since x'yz' + x'yz' = x'yz', because a+a = a) rearrange the equation = x'y'z' + x'yz' + x'yz + x'yz' + x'yz' + xyz' = (x'y'z' + x'yz') + (x'yz + x'yz') + (x'yz' + xyz') = (x'z'(y + y')) + (x'y(z + z')) + (yz'(x + x')) = (x'z'(1)) + (x'y(1)) + (yz'(1)) = (x'z') + (x'y) + (yz') = x'z' + x'y + yz' so, x'y'z' + x'yz' + x'yz + xyz' = x'z' + x'y + yz'
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Please use algebraic manipulation to prove the following
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