Spans of subsets and union of two sets

Question

Is this true or not? How would I prove or disprove this?

If the set of vectors $\{a_1 \dots a_n\}$ spans a subset $S$ and the set of vectors $\{b_1 \dots b_n\}$ spans a subset $T$, then $\text{Span} \{a_1 \dots a_n, b_1 \dots b_n\} = S \cup T$

Answer 1

Hint: Think about vectors in $\Bbb R^2$. Say $n=1$, $a_1=(1,0)$ and $b_1=(0,1)$. What are $S$ and $T$; what is the span of $a_1,b_1$?