Show all of the implications and equivalences between the following relationships.

Question

A: $x=y$, B: $x^2 = y^2$, C: $xy=x^2$, D: $xy=y^2$

The answers are: $$A \implies B$$ $$A \implies C$$ $$A \implies D$$

I don't understand how $A \iff C$ among others is not an answer, there is no way $xy=x^2$ can be true if $x=y$ is not true...

Answer 1

I don't understand how A $\Longleftrightarrow $C among others is not an answer, there is no way $xy=x^2$ can be true if $x=y$ is not true...

Hint: Choose $x = 0$.