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I'm confused with the usage of "of which" in relative clause.
Could anyone please tell me, on what occasion do we use "of which" to describe the subject?
I sometimes saw "each of which" in some sentences as well. I wonder if this "of" has meaning or not, or just appears as a preposition with fixed usage? Thank you very much!
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Hi Phanasy;

The relative pronoun in a clause must fit in the correct grammatical position in its clause. It can be subject, direct object, indirect object, or object of a preposition.

I liked the cake which was decorated with pink icing. (which is the subject of "was decorated")
I liked the cake which Aunt Mary baked. (which is the object of baked.)
I liked the cake, the top of which was peppered with lighted candles. (of which is a prepositional phrase in the clause. Which is the object of the preposition of)
I love Aunt Mary to whom we gave the cake. (Whom is the indirect object of gave.)
The knife with which we cut the cake was very sharp. (Which is the object of the preposition with. )

Does this help?
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Thank you very much for your help
After reading your advices, I think I've understood a lot but still I'm having problems in interpreting the final sentence.

According to your third example, you said "which" is the object of the preposition "of", I wonder whether I got it right or wrong, so this "which" refers to "the top of the cake", that is the "which" is giving further description about the "top" of the cake, is it right?

And for the last sentence,
"The knife with which we cut the cake was very sharp. (Which is the object of the preposition with. )"
I am sorry I don't understand what "with" is referring to. Would you mind giving me more explanation about this?
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PhantasyAccording to your third example, you said "which" is the object of the preposition "of", I wonder whether I got it right or wrong, so this "which" refers to "the top of the cake", that is the "which" is giving further description about the "top" of the cake, is it right?
Which refers to cake. So you can just substitute "cake" for "which"
.... the top of (which =) the cake was peppered with candles.
Phantasy"The knife with which we cut the cake was very sharp. (Which is the object of the preposition with. )"
I am sorry I don't understand what "with" is referring to. Would you mind giving me more explanation about this?

With is a preposition. Examples:
I went with you to the party.
He hit his brother with a stick.
We cut the cake with a knife.

In the example, the "core" of the sentence is:
The knife was very sharp.
Which knife are we talking about? - the knife we cut the cake with!

The knife with which (which substitutes for knife) we cut the cake was very sharp.

AlpheccaStarsIt can be subject, direct object, indirect object, or object of a preposition.
Don't forget, AS, that the relativised element can also be an adjunct of time, place or reason:

the day [when you were born] (adjunct of time)

a place [where you can relax] (adjunct of place)

the reason [why she got angry] (adjunct of reason)

BillJ
Yes, I agree. But the poster's question was specific to "which," and I wanted to concentrate on that one word as much as possible. It was difficult to come up with an example of indirect object, so I did deviate and use who/whom for that case.

Regards,
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Thank you for this great help!
I think I've got the trick in interpreting such relative clause patterns.