How can we prove/disprove if $W=V(x^{2}+x)$ and $T=V(xy)$ ,both subsets of $\mathbb{A}^{2}$, are isomorphic algebraic sets?
At first I wanted to use Corollary $3.7$ page $20$ of Hartshorne's book:
If $X$ and $Y$ are two affine varieties then $X \cong Y$ if and only if $A(X) \cong A(Y)$.
I think $A(W) \cong k[y] \times k[y]$. But we can't use the above result because none are affine varieties, they are clearly reducible.
Any hint? (this is before the chapter about projective varieties).