For any two numbers X and Y , define X#Y=X+Y -XY . If X,Y>0.5, then X#X < Y#Y if
i. 1>X>Y
ii. 1>Y>X
iii. Y>X>1
Choose the correct option
A) i only	B) option ii only	C) i and ii only	D) ii and iii only	E) i and ii only
X#X = 2X-X^2 and Y#Y=2Y-Y^2   X#X &lt;Y#X   =&gt; 2X - X^2 &lt; 2Y - Y^2   =&gt; 2(X-Y) &lt; (X-Y)(X+Y)   =&gt; X+Y&gt;2 and X-Y&gt;0 or X+Y&lt;2 and X-Y&lt;0   =&gt; X+Y&gt;2 and X&gt;Y or X+Y&lt;2 and X<y (i),="" 1="" if="" using="">X&gt;Y, then the first case applies but X+Y&gt;2 is not satisfied. False.   Using (ii), if 1&gt;Y&gt;X, then the second case applies and X+Y&lt;2 is satisfied. True.   Using (iii), if Y&gt;X&gt;1, then the second case applies but X+Y&lt;2 is not satisfied. False.   Therefore only (ii) is true, and choice (option ii only) is correct.</y>
<result>B</result>
For any two numbers X and Y , define X#Y=X+Y -XY . If X,Y>0.5, then X#X < Y#Y if
i. 1>X>Y
ii. 1>Y>X
iii. Y>X>1