Fake can mean not authentic. For example if someone makes a computer and names it Sony but it really isn't Sony, then that would be a fake computer. Socially, in spoken English, fake can mean a person who is not a true friend. "She is so fake", meaning that the person pretends to be your friend but really isn't. I rarely use the word false. The only time I can think of it is in tests, when you have to pick True of False. Meaning not being the true fact. Or for example, if someone gave a false testimony in court, it means that they lied. Change and alter are somewhat similar. If you change something, usually you are just putting on a different item, but if you alter it, you are altering that specific object. Example: I changed my tire. Meaning: I removed my tire and put a new one on. Example: I altered my tire. Meaning: I modified my tire in some way. or Example: I changed clothes. Meaning: I put on different clothing. Example: I altered my clothes. Meaning: I made some modifications to my clothing. Join and enroll are virtually the same. Usually you join or enroll in something like a class, a club, a team. If you "take part in" something, it means you participated, but you may not have officially signed up, joined or enrolled in the activity. And "go in for" just means you went to do something. By my definition, a carpet is what is laid down and it covers the entire room from wall edge to wall edge. A rug is a small piece that can be thrown anywhere. A rug can be put on just a floor, or on top of another carpet.