(a) If V is a vector space and W is a subset of V that is a vector space, then W is a subspace of V.

The given statement does not specify the fields over which V and W are vector spaces.

If V and W are vector spaces over the same field, then they will be closed under the operations addition and multiplication and hence the statement will be true.

(b) The empty set is a subspace of every vector space.

Note that, every vector space contains the zero vector.

Since empty set does not contain any element, empty set is not a vector space.

Hence, empty set is not a subspace.

Therefore, the statement is false.

The given statement does not specify the fields over which V and W are vector spaces.

If V and W are vector spaces over the same field, then they will be closed under the operations addition and multiplication and hence the statement will be true.

(b) The empty set is a subspace of every vector space.

Note that, every vector space contains the zero vector.

Since empty set does not contain any element, empty set is not a vector space.

Hence, empty set is not a subspace.

Therefore, the statement is false.