Consider the following implication, $x,y \in \mathbb R \wedge x \lt 0 \implies \nexists y$ such that $x=y^2$. Question asks to use contrapositive, so here is my proof:
Let $x=y^2$ (since it's negation of conclusion). I want to show that $x \ge 0$.
So from new hypothesis we know that x is positive real number greater than or equal to 0, since $x=y^2$ (x is equal to y square) this means the new conclusion is correct. So contrapositive is true meaning implication is true.
Is my proof correct, or am I missing something?
Edits: Could someone please give me correct proof for this problem? Thanks.