# GATE Papers >> CSE >> 2016 >> Question No 16

Question No. 16

Consider the Boolean operator # with the following properties:

$x\#0\;=\;x,\;x\#1\;=\;\overline x,\;x\#x\;=\;0\;and\;x\#\overline x\;=1.$ Then $x#y$ is equivalent to

##### Answer : (A) $x\overset-y+\overset-xy$

Solution of Question No 16 of GATE 2016 CSE Paper
 x y x#y 0 0 0 0 1 1 1 0 1 1 1 0

$\begin{array}{l}x\#0=x\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;...1\\x\#1=\overline x\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;...2\\x\#x=0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;...3\\x\#\overline x=1\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;...4\\x\#y=x\overline y+\overline xy\end{array}$

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