We often use 'suppose' to mean 'imagine' or 'guess'
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I suppose you'll be meeting Danielle when you go to Paris?
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When you weren't there, I supposed you must have been held up.
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I suppose you two know each other?
Notice that 'suppose' is not normally used in the continuous form. We do not usually say 'I am supposing'.
- Now I suppose we'll have to do something else.
- We're waiting for John and I suppose he must be stuck in traffic.
- At this moment I suppose it doesn't matter.
Notice that for 'imagine not' or 'guess not' that we make 'suppose' negative, not the other verb.
- I don't suppose you know where Mary is?
- I don't suppose he'll do anything.
- I don't suppose you have a Nokia phone charger here?
When responding to an idea with 'suppose', you can use 'so' to avoid repeating the idea that has already been expressed.
- Is Susan coming to this meeting? ~ I suppose so.