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