Is Windows XP compatible with Windows 7?

Answer 1

Not directly they're two different operating systems XP being the older one windows 7 being the new one. But most Xp programs Are compatible With Windows Seven........ In fact I cant think of one that isn't. This is coming from a Basic Programmer.
Both windows xp and windows 7 are independent from each other. If you are asking will a windows XP program run on windows 7 then the answer will vary by program.

There is a compatibility mode in most versions of windows 7 that will make running legacy software possible

Answer 2

It is fully compatible with Windows Vista, and Windows 7 Professional + Ultimate have XP mode, where it boots XP like an application.