GATE | GATE CS Mock 2018 | Set 2 | Question 44
If w, x, y, z are boolean variables, then which of the following in CORRECT?
(A) wx + w(x+y) + x(x+y) = w + xy
(B) (wx'(y + z’))’ + w’x = w’ + x + y’z
(C) (wx'(y + xz’) + w’x’)y = xy’
(D) (w + y)(wxy + wyz) = wxy + xyz
Answer: (B)
Explanation: (A)
wx + w(x+y) +x(x+y) = wx + wx + wy + x + xy = wx + wy + x + xy = x(w + y + 1) + wy = x + wy
(B)
(wx’(y + z’))’ + w’x = w’ + w’x + y’z = w’ + x + y’z
(C)
(wx’(y + xz’) + w’x’)y = wx’y + wx'xz'+ w’x’y since x'x = 0 = wx’y + w’x’y = x’y(w + w') = x’y
(D)
(w + y)(wxy + wyz) = wxy + wyz(w + y)(wxy + wyz) = wxy + wyz
So, option (B) is correct.
Quiz of this Question
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