The simplified form of the Boolean expression (X + Y + XY)(X + Z) is A. X + Y + Z B. XY + YZ C. X + YZ D. XZ + Y E. None of the above

The correct answer is $\boxed{\text{C. }X + YZ}$.

To simplify a Boolean expression, we can use the following rules:

• $A + A = A$
• $A +
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  A’ = 1$
• $A’ + A = 1$
• $A + B = B + A$
• $A(B + C) = AB + AC$
• $(A + B)C = AC + BC$
• $A’B = A’B$
• $AB’ = A’B’$

We can use these rules to simplify the expression $(X + Y + XY)(X + Z)$ as follows:

• $(X + Y + XY)(X + Z) = (X + Y)(X + Z) + (XY)(X + Z)$
• $= X(X + Z) + Y(X + Z) + XY(X + Z)$
• $= X^2 + XZ + YX + YZ + XY^2$
• $= X^2 + XZ + YX + YZ + XY + YZ$
• $= X^2 + (X + Y)Z + YZ$
• $= X^2 + YZ$

Therefore, the simplified form of the Boolean expression is $\boxed{\text{C. }X + YZ}$.

Here is a brief explanation of each option:

• Option A: $X + Y + Z$. This is not the simplified form of the expression, because it does not include the term $YZ$.
• Option B: $XY + YZ$. This is not the simplified form of the expression, because it does not include the term $X$.
• Option C: $X + YZ$. This is the simplified form of the expression, because it includes all of the terms in the original expression.
• Option D: $XZ + Y$. This is
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  not the simplified form of the expression, because it does not include the term $YZ$.
• Option E: None of the above. This is the correct answer, because none of the other options are the simplified form of the expression.