Could anyone please help me with this question?
(1) Let $(E, p, B)$ be a vector bundle where $E$ is the total space, $B$ is the base, and $p$ is the structure map, that is, $p:E\to B$. Now suppose $E'$ is a subspace of $E$, $B'$ is the subspace of $B$, and $p'$ is the restriction of $p$ to $E'$. If the image of $p'$ is contained in $B'$, then show $(E', p', B')$ is a vector bundle. (2) Prove or disprove: Let $s$ be a section of $(E, p, B)$. Then restriction of $s$ to $B'$ is a section of $(E', p', B')$ if and only if $s(b)$ is in $E'$ for each $b$ in $B'$.
THANK YOU SO MUCH IN ADVANCE.