Suppose is to assume something when you are not completely sure. It is like a "what if..." word. for example: "Suppose the dog bit him." would be the same as "What if the dog bit him." It could also mean you are required to do something: for example: "He is supposed to be studying." is the same as "He has to study."

"suppose" represents your prediction, your thought about something. For ex: I suppose he goes to school today! Sometime you use "suppose" for your definition about somebody or something at one point of time. For ex: He's supposed to be a doctor! The pencil is supposed to be in the bag! That's just what I thought) Looking for a better answer :D

To "suppose" means to assume something is true, without knowing. "I was going to steal, but I suppose it would be against the law." "He was supposed to be here" means "People would suppose him to be here". In that way, "supposed to" is the same as "meant to" or "expected to".