If we add the word "Either" to the sentence, we get
"Either John or Jim goes there every day"
which means that one person, not both, goes there every day.
If we omit the word "Either" from the sentence, we get
"John or Joe goes there every day"
which means that one person, not both, goes there every day. The same meaning as above.
"Either...or" is a set called a correlative conjunction. We can omit "Either" from the set without changing the function of "Either...or". For example:
Sam: Does anyone go to the gym across the street?
Pat: John or Joe (I'm not sure which guy) goes there every day.
We could also say that "It's" and "that/who" have been omitted as well:
Pat: It's (either) John or Jim that/who goes there every day.
But those omissions do not change the function of "or".
Well, "or" is not like "and".I think some people (may-be most people) say "go" instead of "goes". I wonder if that is correct according to traditional grammar, ...
"and" is a coordinating conjunction. It joins two like elements into one element.
"or" is a correlative conjunction. It gives us a choice of picking one phrase or the other, not both.
Unlike "and", "or" has nothing to do with subject-verb agreement. It's the word/phrase closest to the verb that determine number agreement. For example,
1. (Either) John or Jim is coming to the party.
2. It's (either) the bananas or the oranges that are on sale today.
3. (Either) your father or your sisters are going to have to drive me to work.
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