1 is false, take for example the sets {v} and {2v}
2 is true, in general the subset of a linearly independent set is linearly independent. Think a bit on how to prove this, but it's pretty straightforward.
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thorny mesa
Take any vector of s1 inter s2, it is a vector that can’t be expressed as a combination of the other vectors necessarily, because all of these vectors are linearly independent between each other, they are part of s1 and s2 so by definition s1inters2 is linearly indépendant