Chapter 4.3, Problem 43E

True or False? In Exercises 43 and 44, 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.

$\left(\text{a}\right)$ If $W$ is a subspace of a vector space $V$, then it has closure under scalar multiplication as defined in $V$.

$\left(\text{b}\right)$ If $V$ and $W$ are both subspaces of vector space $U$, then the intersection of $V$ and $W$ is also a subspace.

$\left(\text{c}\right)$ If $U$, $V$, and $W$ are vector spaces such that $W$ is a subspace of $V$ and $U$ is a subspace of $V$, then $W=U$.