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.


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