If $V=V_1\oplus V_2 = V_3 \oplus V_4$, then are $V_1$ and $V_3$ isomorphic? Same question with $V_2$ and $ V_4$

Question

Let $V$ be a vector space on a field or characteristic $0$. Also, let $V_1, V_2, V_3$ and $V_4$ be subspaces of $V$ such that $$V=V_1\oplus V_2 = V_3 \oplus V_4.$$

Obviously, if $X$, $Y$ and $Z$ are dubspaces of $V$ such that $X \oplus Y = X \oplus Z$ since $X \cong V/Y$ and $Y \cong V/X$ and so $$Y \cong V/X \cong Z.$$

My question is: Can this be generalized a little bit. I.e. if $V=V_1\oplus V_2 = V_3 \oplus V_4$ the $V_1 \cong V_3$ and $V_2 \cong V_4$? Or do I need some conditions about those four subspaces.

Thanks for your help!

Answer 1

Consider $V_1 = V_2 = \mathbb{R}^2,\ V_3 = \mathbb{R},$ and $V_4 = \mathbb{R}^3.$