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!