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