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Note that because every 2-element subset chosen from a set of 5 elements corresponds to a unique 3-element subset consisting of the elements not chosen.

My questions concern whether consisting of the elements not chosen is a relative clause (transormed from: subest which consists of...) or is the gerund a object complement.

The number of digits to the right of the decimal point is equal to the sum of the numbers of digits to the right of the decimal points in the number being multiplied.

Is being multiplied a reduced relative clause(transformed from: the number which is being multiplied) or is the gerund an object complement?

I have trouble making a distinction because the following website says (https://www.thefreedictionary.com/Object-Complements.htm):
"Participles generally function as object complements by describing what the direct object is or was doing."

  • Initial point: there are no objects in your examples, so there can't be any object complements. In any case, object complements can only be NPs or AdjPs. In both your examples, the clauses in question are gerund-participial ones modifying the preceding noun. They have the same meaning as the corresponding relative clause, but we don't call them relative clauses because there is no possibility of them containing a relative phrase, cf. *"subset which consisting of the elements not chosen". – BillJ Mar 7 '19 at 14:23
  • I've just posted a full answer for you. – BillJ Mar 8 '19 at 7:01
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Note that because every 2-element subset chosen from a set of 5 elements corresponds to [a unique 3-element subset consisting of the elements not chosen].

The number of digits to the right of the decimal point is equal to the sum of the numbers of digits to the right of the decimal points in [the number being multiplied].

There are no objects present in these sentences, so there can't be any object complements. In any case, object complements can be NPs or AdjPs, but never clauses, e.g. They elected him president / I consider Ed highly untrustworthy.

The bracketed elements are noun phrases in which the gerund-participial clauses (in bold) are in modifying function. Semantically, they are similar to relative clauses, cf. a unique 3-element subset which consists of the elements not chosen. But we don't call them relative clauses because there is no possibility of them containing a relative phrase: we can't say * a unique 3-element subset which consisting of the elements not chosen.

  • Thank you again so much , the answer is really helpful. – Peilin Mar 8 '19 at 14:00

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