Question 303713
Well if x > y, then {{{x<>y}}}. So if {{{x(x - y) = 0}}}, then either {{{x=0}}} or {{{x-y=0}}} giving {{{x=y}}}. But we just said that {{{x<>y}}}. So we can only say that {{{x=0}}}. So statement I is true.



If {{{x=0}}}, then just plug this value into {{{x>y}}} to get {{{0>y}}} which shows us that statement II is true.



Finally, if {{{x>y}}}, then subtracting 'x' from both sides gets us {{{0>y-x}}} which is the opposite of {{{y-x>0}}}. Alternatively, assume that {{{y-x>0}}} is true. Solve for y to get {{{y>x}}}. This is the opposite of {{{x>y}}}. So statement III is false.