Intersection/ union of a set of transitive relations

Hi, I'm a bit stuck on the following question:

Assume $\displaystyle \mathcal{A}$ is a non-empty set, every member of which is a transitive relation. (a) Is the set $\displaystyle \bigcap\mathcal{A}$ a transitive relation?

(b) Is the set $\displaystyle \bigcup\mathcal{A}$ a transitive relation?

I started my solution with the following:

$\displaystyle R\in \mathcal{A} \Rightarrow (aRb \wedge bRc \Rightarrow aRc)$

$\displaystyle \bigcap \mathcal{A} = \{ a \mid \forall R \in \mathcal{A} , a \in R \} = \{ a \mid ( aRb \wedge bRc \Rightarrow aRc ) a \in R \}$

After that I don't really know what to do. Please could someone point me in the right direction?

Also one more problem:

Let $\displaystyle \mathcal{A} $ be a set of functions such that for any *f *and any *g* in $\displaystyle \mathcal{A} $, either $\displaystyle f \subseteq g$ or $\displaystyle g \subseteq f$. Show that $\displaystyle \bigcup \mathcal{A}$ is a function.

I'd really appreciate any help,

Many thanks steph