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Question 1:

Two definitions of "and":

1.(used to connect grammatically coordinate words, phrases, or clauses) along or together with; as well as; in addition to; besides; also; moreover

2.also, at the same time:

My questions is, is the second definition only for when two things are happening simultaneously, while the first definition is for everything else?

To clarify, would this be correct?

"I sat in my chair and talked about the weather" (Definition 2)

"I watched you and John play" (Definition 1)

Question 2:

'take X and do Y"

is "and" being used in the above example as a way to separate the two clauses chronologically?
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1-- No, I don't think so. 'And' has more than 2 meanings, in the first place:

1.(used to connect grammatically coordinate words, phrases, or clauses) along or together with; as well as; in addition to; besides; also; moreover: pens and pencils.


2.added to; plus: 2 and 2 are 4.


3.then: He read for an hour and went to bed.


4.also, at the same time: to sleep and dream.


5.then again; repeatedly: He coughed and coughed.


6.(used to imply different qualities in things having the same name): There are bargains andbargains, so watch out.


7.(used to introduce a sentence, implying continuation) also; then: And then it happened.


8.Informal . to (used between two finite verbs): Try and do it. Call and see if she's home yet.


9.(used to introduce a consequence or conditional result): He felt sick and decided to lie down for awhile. Say one more word about it and I'll scream.


10.but; on the contrary: He tried to run five miles and couldn't. They said they were about to leaveand then stayed for two more hours.


11.(used to connect alternatives): He felt that he was being forced to choose between his careerand his family.


12.(used to introduce a comment on the preceding clause): They don't like each other—and withgood reason.

"I sat in my chair and talked about the weather" (Definition 1 and 4) "I watched you and John play" (Definition 1)

2-- 'take X and do Y"- Definition 3

Comments  
I know that there are more than two definitions of "and".

But it seems like you agree with my examples?