Suppose U and V are subspaces of a vector spaces W. (a) (5 points) Prove that...

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Suppose U and V are subspaces of a vector spaces W. (a) (5 points) Prove that the intersection U nV is a subspace of W. (b) (5 points) Is the union UUV necessarily a subspace of W? Prove or provide a counterexample. Suppose U and V are subspaces of a vector spaces W. (a) (5 points) Prove that the intersection U nV is a subspace of W. (b) (5 points) Is the union UUV necessarily a subspace of W? Prove or provide a counterexample.