Is it true that $ U \oplus W_1 = U \oplus W_2 \implies W_1 = W_2 $?

Question

Is it true that if $ U \oplus W_1 = U \oplus W_2 $, then $ W_1 = W_2 $? I think that if $ U \oplus W_1 = U \oplus W_2 $, then $u+w_1=u+w_2$, so $W_1=W_2$. But did I make any mistakes?

Answer 1

Just consider $V=\mathbb R^2$, $$U=\{(x,0)\mid x\in \mathbb R\}\\W_1=\{(0,y)\mid y\in \mathbb R\}\\W_2=\{(y,y)\mid y\in \mathbb R\}$$