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If true give proof of answer, if false, give an example disproving the statement.

2. My thoughts: If U is a subspace of V, then the zero vector is in V. As well as

**x**+

**v**is in V and

*a*

**x**is in V (by definition of a subspace). If these three are in V, and V is in W, then these three must be in W as well. Therefore U will be a subspace of W. However, I don't know if there is an example to disprove this, or if my logic is completely flawed.

Thanks for any help!