Yes, they do
Does this imply that 'she' cannot 'set out to do the work now' and 'you' will not 'meet her at the airport tomorrow morning'?
No. The meaning of "subjunctive" is often given as "contrary to fact". But it's really harder to pin down than that. When you say "I'd rather ..." then there is obviously some other proposition currently in force. You are suggesting an alternative and contrary proposition. That's what makes it subjunctive. Note you could also use "prefer" for "rather" here.
What's the difference between the following sentences?
(3) I'd rather have left a note on her desk.
(4) I'd rather left a note on her desk.
(5) I'd rather I left a note on her desk.
4. and 5. are wrong. 3. sounds strange.
It sounds strange to say you would rather have done something different.
It would be better to say "I should have left a note on her desk" or "I wish I'd left a note on her desk".
In speaking of someone else, you could say "I would have preferred he left a note on her desk". A stronger version would be "He should have left a note on her desk".
Note it's stronger to say "He should have done ..." than "I should have done..." - because in the former, you're making a criticism of his actions. In the latter, you mean simply what you've written in 3.
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