Difference between some sentences involving tense

Question

What is the difference between the two sentences in each of the three cases?

1A. I should like to have sat down.

1B. I should have liked to sit down.

2A. He acts as if he knows the subject.

2B. He acts as if he knew the subject.

3A. He felt better when she gave him medicine.

3B. He was feeling better when she gave him medicine.

The first pair confounds me the most.

Answer 1

For the first pair, you might like to take a look at this question and the answers. Based on the methodology I used in my own answer there, in A I should like refers to the time of speaking and to have sat down refers to some previous time. In B, on the other hand, I should have liked refers to the same time as the sitting down.

In the second pair, A suggests that the speaker does know the subject, while B suggests that the speaker might not.

In the third pair, A suggests that the medicine made him feel better, while B suggests that he was feeling better before she gave him the medicine.

All of these explanations should be read with a certain amount of caution. Much will depend on the circumstances in which they are being said or written.