For all numbers p and q, the operation @ is defined by p@q = p^2 - pq. 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 from the following options.
A) II B) I and II C) I and III D) II and III E) All of the above
p@q = p^2 - pq=p(p-q).... so p@q will be zero if p=q or p=0.. but a 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 ans I and II....
<result>B</result>
For all numbers p and q, the operation @ is defined by p@q = p^2 - pq. If xy ≠ 0, then which of the following can be equal to zero?
I. x@y
II. (xy)@y
III. x@(x + y)