For all numbers u and v, the operation @ is defined by u@v = u^2 - uv. If xy ≠ 0, then which of the following can be equal to zero?
I. x@y
II. (xy)@y
III. x@(x + y)
Choose the correct choice.
A) II	B) I and II	C) I and III	D) II and III	E) All of the above
u@v = u^2 - uv=u(u-v).... so u@v will be zero if u=v or u=0.. but u cannot be equal to 0.. as per Q, x and y can take any int value except 0...   now lets look at the choices..   when x=y, it will be 0... so ok...   when we put xy=y, it is possible when x=1 and y any integer... so ok again   when we put x=x+y.... only possibility when y=0 and it is given x and y cannot be 0....so not possible   only l and ll possible   answer: I and II
<result>B</result>
For all numbers u and v, the operation @ is defined by u@v = u^2 - uv. If xy ≠ 0, then which of the following can be equal to zero?
I. x@y
II. (xy)@y
III. x@(x + y)