I'm not a native speaker,trying to understand few things.

Here soda is an object. soda has some properties like colour, taste, name ,price.

The Taste of soda.
The Colour of soda.
The Name of soda.
The Price of soda.

Now the question is: Why would we say-

"The family of 3".

Here "3" is an object but It doesn't have a property family.

"she is the girl of my dream"

"Dream" doesn't have a property called "the girl".

I'm trying to understand how come girl is related to dream and family is related to 3.

  • 1
    "of" has many meanings. A non-random sample of dictionaries shows of (10 definitions), and of (21 definitions). – user3169 Jul 12 '16 at 17:14

Prepositions in English are complex, and of is no exception. It can be used to indicate multiple different relations. Definitions are from Google's definition of of.

The taste of soda

The colour of soda

The price of soda

All these indicate "an association between two entities, typically one of belonging". In these cases, there's a taste, a colour and a price that belong to soda.

The family of 3 (people)

This indicates "the material or substance constituting something". In this case, a family is made of 3 people.

She is the girl of my dreams.

This also indicates "an association between two entities, typically one of belonging." The girl metaphorically belongs in one of the speaker's dreams.

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