Intersection/ union of a set of transitive relations

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

Assume is a non-empty set, every member of which is a transitive relation. (a) Is the set a transitive relation?

(b) Is the set a transitive relation?

I started my solution with the following:

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

Also one more problem:

Let be a set of functions such that for any *f *and any *g* in , either or . Show that is a function.

I'd really appreciate any help,

Many thanks steph