Suppose and Assume mean basically the same thing - taking something as fact without any proof of such - however I always consider assume to be a bit more formal, a phrase you would use in a working environment, whereas suppose is something I would use in an informal setting. I hope this helps :)

"I suppose" and "I assume" mean almost the same thing, and sometimes either can be used. But "suppose" is more tentative and indicates less certainty, while "assume" means that one is taking something as fact, with or without evidence. (like, a politician's supporters assume what he says is true.)

There is a slight difference in meaning. To "assume" means to take for granted that something is true. For example, you might say, "she smiled at me, so I assumed she was happy to see me". You might also say, "I assume she is coming because she called me". People assume things when there is a degree of evidence. To "suppose" means to think or imagine that something is true without cause. People often say, "I suppose you know what you are doing" when they are not really sure at all. People also say, "I suppose so" in a reluctant way. For example, when asked if you want to try a new restaurant, "you might say, "I suppose so" because you are unsure. Your friend might say, "I assume it is a nice place because I read a good review about it in a magazine". Hope this helps

It's a little difficult because by definition they are almost the same, but in spoken usage I feel they are not always interchangeable. For example, I would not interchange them in these sentences: "I assume you can be there on time, right?" "I suppose I'll go since I have nothing else to do"

The answer is: "I supposed to be there" and "I assumed that he did it". Thanks.