If * denotes a mathematical operation, does X * Y= Y *X for all x and y?
( 1) For all x and y, x * y= 2( x^2 + y^2) - Statement One is Enough.
( 2 ) For all y, O * y= 2y^2. - It's not sufficient but why?
ETS's crappy explanation.
There are many possible definitions of x * y for which 0 * y= 2y^2- for example x *y= x + 2y^2 or x *y= ( x + 1)( 2y^2). If we consider x *y= x + 2y^2 and then y * X = y + 2x^2. But it is not true that x + 2y^2= y + 2x^2.
Now, it would help if they were more concrete.
But, I think I saw this somewhere before on ETS's symbolism.
When they turn around X* Y to Y * X, they mean for Y *X and that Y takes that part of X and X takes the part of Y, etc.
I'll let Bogdan explain.