Which are the correct equations? Due to my knowledge seems to be the 1st one is correct, but the others I can't figure out.

$$\begin{array} {lrcl}
\text{(1).}~ & \forall x \in \mathbb R ~\forall y \in \mathbb R &:& y=2x+1 \iff x= \frac{y-1}{2} \\
\text{(2).}~ & \forall x \in \mathbb R ~\forall y \in \mathbb R &:& y^2-y+x^2-x=0 \iff (x=y \land x=0) \\
\text{(3).}~ & \forall x \in \mathbb R ~\forall y \in \mathbb R &:& (x=y \land x=0) \implies y^2-y+x^2-x=0 \\
\end{array}$$

Can anyone help me to solve this question? Thanks
P.S.-(Sorry to say that above question is wrong due to my mistake.I re-edited the question.plz help!)