A set $(u,v,w)$ of vector is linearly independent if $u$ is not a linear combination of $v$ and $w$.
It's false since if you take: $$ \{ u = (1,0), \, v = (0,1), \, w = (0,0) \}, $$ this set is dependent but $u$ doesn't span $\{v, w\}$.
The part I don't get is why does $u$ not span $\{v, w\}$ and what makes the set $\{(1,0), (0,1), (0,0)\}$ dependent?
Thanks everyone