Students who are unsure whether to use the definite or the indefinite article before a noun often try to camouflage this by using possessives. For example, instead of:

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I borrowed a book.

they may say something like:

I borrowed Peter’s book.

 

and there is no need to think about whether the borrowed item is “a book” or “the book”. The reason why there is no article in the latter sentence is that Peter’s replaces it in the very same way as possessive pronouns do; we could also say “I borrowed his book”, for example.

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However, there is a catch. Some students, lured by the absence of articles after a possessive and the fact that there are no articles before proper nouns, mistakenly believe there are never any articles at all around possessives.

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In fact, articles are used in the same way before possessives as before any noun that doesn’t have an ’s. We don’t say “the Peter’s book” simply because we don’t say “the Peter”, but “teacher” is always either “a teacher” or “the teacher”, so we would say:

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correct -----> He borrowed the teacher’s book.

wrong ----> He borrowed teacher’s book.

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correct ----> Sometimes a student can be a teacher’s nemesis.

wrong ----> Sometimes a student can be teacher’s nemesis.

 

Since we usually don’t use articles before mass nouns, we wouldn’t use them before the possessive form of a mass noun either. Note, however, that in this case it is much more common to use the construction “of X” instead of “X’s”:

 

correct ----> Soap enhances the cleaning ability of water. (most common)

correct ----> Soap enhances water’s cleaning ability. (possible)

wrong ----> Soap enhances a water’s ability to clean.

 

Finally, care should be taken when using established phrases with possessives, which often lack the article although it would normally be used, for example:

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Could you please say it in layman’s terms?

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External Link : https://jakubmarian.com/articles-before-possessive-s/#:~:text=In%20fact%2C%20articles%20are%20used,He%20borrowed%20the%20teacher's%20book.