Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.(a) If W is a subspace of a vector space V, then it has closure under scalar multiplication as defined in V.(b) If V and W are both subspaces of a vector space U, then the intersection of V and W is also a subspace.(c) If U, V, and W are vector spaces such that W is a subspace of V and U is a subspace of V, then W = U.

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Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.
(a) If W is a subspace of a vector space V, then it has closure under scalar multiplication as defined in V.
(b) If V and W are both subspaces of a vector space U, then the intersection of V and W is also a subspace.
(c) If U, V, and W are vector spaces such that W is a subspace of V and U is a subspace of V, then W = U.

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