Q1. What's the difference between the following A) and B)? Is there any difference in the meaning?
Q2. If the meaning is the same, which is more appropriate in formal writing?

A) The operation and the behavior of this machine
B) The operation and behavior of this machine

Q3. In the case of B), is the verb which follows after the subject going to be "is" or "are"?

Q4. According to one article, it says: "Parallelism requires that an article (a, an, the) or preposition applying to all members of a series must either appear before the first item only or be repeated before each item." Is this (Can this be) applied to the above A) and B) as well?

Please help me clear the above 4 points.
1 2
1-- No difference
2-- either is appropriate
3-- are
4-- yes, it is applied to A and B
Q1: No, I don't think there's any difference between A and B.

Q2: In any setting, it's usually better to avoid repetition. A sounds more formal to me, but both A and B would work in formal writing.

Q3: I think the verb should be "are" any time you have a compound subject with the word "and". Examples: The table and (the) chair are new. The dog and (the) cat are outside.

Q4: Your examples A and B are both correct according to that rule of parallelism. If there were three nouns in the subject, for example, you'd have to write either:

"The table, the chair, and the lamp are new" or "The table, chair, and lamp are new."

According to that rule, it would be incorrect to write "The table, the chair, and lamp are new" or "The table, chair, and the lamp are new."

I hope that helps! Let me know if you have any more questions. Emotion: smile
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I'd like to offer a small comment that is off the main point of the thread.

The operation and the behavior of this machine

To me, it sounds awkard to talk of a machine's 'behaviour'. This is much more commonly a word for people/animals.

I'd say something like the operation and functioning of this machine.

Best wishes, Clive
Q3. If the author views 'the operation' and 'the behavior' as a one set, can we use 'is'?

If the author views them as one set, then s/he will use is, yes.

However, whether it is accepted by the reader (who may be the essay teacher) is another matter. Fundamentally, all 'rules' of the language (as here in the case of a compound subject) depend on an understanding and agreement between producer and receiver. If it is reasonable to both that operation and behaviour/functioning (which I now see, thanks to Clive, are all actually synonymous, so that our compound subject is in fact redundant) are a single set, then the singular verb works; but if the writer thinks they're a set while the reader does not envision them thus, then communication has (to a slight extent at least) failed, and the reader takes it as confusing or incorrect S-V concord.
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Thank you for all of your advice/comments.
Now I understood fully.
Thank you.

Is this correct?

Our furniture is a table, chair and lamp. (Note that there are no articles in front of the last two words.)

Thank you again.
Yes, that sentence is grammatically correct. It sounds somewhat awkward, though; we don't usually say "our furniture is" in that context. "We have a table, chair and lamp" would sound better.
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