The possessive s [closed]

My problem is about the possessive s (the ownership s) not that ending-s.

For example, we say, America's Flag, here the America has gotten one ownership s that is America is the owner of that Flag. And also we say, Computer Science, here that Computer doesn't get the ownership s (why?) even though we talk about Science which is of Computer (here).

My question is when we should add that s to the end of the first name which appear to be the owner of the second name? Or how we can recognize what names get that s, please?

Solution 1:

That is because computer is used adjectival to science.

You could say that the noun computer "acts as" an adjective.

It is the same thing that happens in other compound nouns, like

history teacher
ticket office
race horse

Actually, the science does not belong to the computer (my computer is unable to show me any science that it possesses!) but rather, the science is about computers.

Whenever in doubt, ask yourself if you are actually expressing ownership. If not, there is no s:

John's store is a candy store. (John owns the store, candy does not own the store.)
Pete's prize is the Nobel Prize. (Pete won the prize, but Nobel gave his name to it)

Solution 2:

In the case of Computer Science, the science doesn't belong to a computer. The word "computer" here is being used as a modifier - effectively an adjective - to make the word science more specific.

Solution 3:

Indefinite names don't get possessive s (the ownership s).

Like Computer Science. (Computer is indefinite).

Definite names (like proper names) get possessive s (the ownership s).

Like America's Flag. (America is Definite).

Edits:

"What about "the cat's pajamas"? – Samuel Edwin Ward"

Me: Well, the cat is definite name, because you use "the" article before that.