GATE | GATE-CS-2017 (Set 2) | Question 44

If w, x, y, z are boolean variables, then which of the following in INCORRECT?

(A) wx + w(x+y) + x(x+y) = x + wy
(B) (wx'(y + z’))’ + w’x = w’ + x + y’z
(C) (wx'(y + xz’) + w’x’)y = xy’
(D) (w + y)(wxy + wyz) = wxy + wyz


Answer: (C)

Explanation: 1.)

 wx + w(x+y) +x(x+y)
= wx + wx + wy + x + xy
= wx + wy + x + xy
= x(w+y+1) + wy
= x+wy

2.) 
(wx’(y+z’))’ + w’x
= w’ + w’x + y’z
= w’ + x + y’z

3.) 
(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 thus false

no need to check option 3


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