This question already has an answer here:
I hope that I translated it correctly, correct me if I'm wrong :)
Let $V_1$ and $V_2$ be sub spaces of $L$.
Prove that $V_1\cup V_2$ is a vector sub space if and only if $V_1 \subseteq V_2$ or $V_2\subseteq V_1$
I was thinking of assuming it is correct and taking $2$ vectors from each subspace such that: $$ t_1 \notin V_2 , t_2 \notin V_1 \\ t_1,t_2 \in V_1 \cup V_2 $$ Then : $$t_1 + t_2 ∈ V1$$
This is where I am unsure how to explain my moves...
The teacher said it is incorrect, do you guys have any hints then, perhaps on how to refine a better mathematical 'language of reasoning' too? I am new at this whole math world :)