If \( w, y, z \) are Boolean variables,... - Solved

Question 45

Computer Awareness Boolean algebra Easy

If \( w, y, z \) are Boolean variables, then which of the following is incorrect?

(A) \( w x+w(x+y)+x(x+y)=x+w y \)

(B) \( (w \bar{x}(y+\bar{z}))'+\bar{w} x=\bar{w}+x+\bar{y} z \)

(C) \( (w \bar{x}(y+x \bar{z})+\bar{w} \bar{x}) y=x \bar{y} \)

(D) \( (w+y)(w x y+w y z)=w x y+w y z \)

✓ Correct Answer: Option C Verified Solution

Simplify each one:

(A) \(wx + w(x+y) + x(x+y) = wx + wx + wy + x + xy = x + wy\). Correct.
(B) \((w\bar{x}(y+\bar{z}))' + \bar{w}x = \bar{w} + x + \bar{y}z + \bar{w}x = \bar{w} + x + \bar{y}z\). Correct.
(C) \((w\bar{x}(y + x\bar{z}) + \bar{w}\bar{x})y\). Here \(w\bar{x} \cdot x\bar{z} = 0\), so this is \((w\bar{x}y + \bar{w}\bar{x})y = w\bar{x}y + \bar{w}\bar{x}y = \bar{x}y\). The option says \(x\bar{y}\), so it is incorrect.
(D) \((w+y)(wxy + wyz) = wxy + wyz + wxy + wyz = wxy + wyz\). Correct.

Answer: (C)

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