Is there any difference in meaning or tone between these two and are they even both valid to begin with:
I suppose you don't have the keys with you?
I don't suppose you have the keys with you?
Is there any difference in meaning or tone between these two and are they even both valid to begin with:
I suppose you don't have the keys with you?
I don't suppose you have the keys with you?
They are both valid, though I would be more likely to use the second one. Both are often used in the hope that you do actually have the keys. Logically, if I was supposing nothing at all about the keys, I could use the second but not the first, and so the first sounds more pessimistic to me. In practice though they are often pretty much interchangeable.