T/F prove...
a)The intersection of any two subsets of V is a subspace of V
b) If V is a vector space other than the zero vector space, then V contains a subpace W such that W doesnt equal V.
can sum1 provide a proof for these?
The intersection of two subspaces is again a subspace, correct.
Not true, consider a vector space with dimension 1, then any subspace must have dimension 1 also, because it cannot be larger and it cannot be less because it is 1.b) If V is a vector space other than the zero vector space, then V contains a subpace W such that W doesnt equal V.
can sum1 provide a proof for these?