From any two numbers $$x$$ and $$y$$, we define $$x* y = x + 0.5y - xy$$ . Suppose that both $$x$$ and $$y$$ are greater than 0.5. Then
$$x* x < y* y$$ if

$$x*x < y*y$$
or $$x + 0.5x - x^2 < y + 0.5y - y^2$$
$$y^2 - x^2 + 1.5x - 1.5y < 0$$
$$(y - x)(y + x) - 1.5 (y - x) < 0$$
$$(y - x)(y + x -1.5) < 0$$
$$(x - y)(1.5 - (x + y)) < 0$$
Now there will be two possibilities
$$x < y$$ and $$(x + y) < 1.5$$ ...........(i)
or $$x > y$$ and $$(x + y) > 1.5$$ ............(ii)
Among all options only option B satisfies (ii).
Hence, option B is the correct answer.