OUCH!!! This is a difficult one. I just looked in an electronic dictionary and there were over 90 definitions of up and over 60 definitions of down. There are many, many idioms with the word up, not as many (but still a large number) with down. We tend to learn these as idioms and not as usages of the definitions. I would say your best way to master these is to use an idiom website as there is no way to give you rules and no way to think of all of the terms that use up or down (and they would take up a lot of space in a message!). I take no responsibility for this site, but here is one link to an idiom website with close to 4,000 idioms (I did not look to see if any of them contained up or down, but I am sure they will be there). http://www.usingenglish.com/reference/idioms/ And since you asked, if you want to make someone happy - "You want to cheer them up." If you want someone to make themselves happy and to get out of a depressed mood, you say "Cheer up." If you want to say these terms without up they would be - "You want to make them cheerful." and "Get some cheer." Finally, as you come across idioms with "up" or "down" ask more questions and I am sure we will be happy to answer! So, "Cheer up! We are here to help. Don't let the ups and downs break you down. Or for that matter, do not let them break you up!" Okay, that meant "Be happy. We are here to help. Don't let the bumps in the road worry you. Or for that matter, do not let them make you lose control!"

To feel sad is referred to as being "down", so the opposite of this is "cheer up". "Up" is used as it refers to the sense of the phrase. We think of being happy as something that is as at a high level metaphorically, rather than a low one. The same principle is applied to other things such as "wake up".

Thanks Katya, I'll check it out.

Hello, Alex, I just want to recommend you an entry by Jeff, it is a very interesting one about "up"s. :)) http://www.italki.com/notebook/entry/128896.htm