The simplified form of the Boolean expression (X + Y + XY) (X + Z) is
2023
The simplified form of the Boolean expression (X + Y + XY) (X + Z) is
- A.
XY + YZ
- B.
X + YZ
- C.
XZ + Y
- D.
More than one of the above
- E.
None of the above
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Correct answer: B
Step 1: Simplify the expression (X + Y + XY). We know that Y + XY = Y(1 + X) = Y, since 1 + X = 1 in Boolean algebra. So, (X + Y + XY) = X + Y. Step 2: Multiply (X + Y) by (X + Z). (X + Y)(X + Z) = X(X + Z) + Y(X + Z) = X + XZ + XY + YZ. Step 3: Simplify the result. X + XZ + XY + YZ = X(1 + Z + Y) + YZ = X + YZ, since 1 + anything = 1. Thus, the simplified form is X + YZ.