Quote:
Originally Posted by SkyWatcher  for problem two i think it is useless to proove anything about U S and T when they are the empty set because they have no element so we cannot say anything about the product of two element of such set.
usualy set closed by order are groups (which are none empty) or that sort of thing
beter look to the definition of a set closedby multiplication to see if it admits empty set by definition but demonstration is useless about what do or do not elements of the empy set! |
What are you saying? The sets
are not necessary empty. For example, take
. And take
. Their intersection is empty and union is
. Furthermore, they obey the property that the product of any three elements is again in the set!
Also, an empty set is closed. Because the condition is
. This is a true statement.
See Here.