Of doing

What two elements or which two elements?

JigneshbharatiHow do we know "of"' is a preposition?

Of is always a preposition, or a particle in a phrasal verb. I have never seen it used as a verb, noun, adverb or adjective.

Perhaps this will be a clearer example. The prepositional phrase is underlined.
I am tired of his doing nothing. He just sits in front of his computer, play

Thanks. Does it connect "doing" to "tired"?

Jigneshbharati Does it connect "doing" to "tired"?

I am not sure about your question.
The phrasal verb is "tired of". The complement (object) of this verb is frequently a gerund.

I am tired of sitting. Let me stand up.
I am tired of your complaining. Be quiet!
I am tired of eating rice for breakfast, lunch, and dinner. Let's have grit

JigneshbharatiHow do we know "of"' is a preposition?

It's always a preposition. It doesn't know how to be anything else.

Thanks . I am just confused as how to differentiate that "of" is not a pure preposition but it's a part of phrasal verb?

AlpheccaStarsThe phrasal verb is "tired of".

OOPS My goof.

"Tired" is better described as an adjective (past participle of the verb "tire"), ad CJ rightly said.

The phrasal verb is possible, but uncommon: He quickly tires of one girl friend and finds another.
See entry #4:

Jigneshbharati Thanks . I am just confused as how to differentiate that "of" is not a pure preposition but it's a part of phrasal verb?

be tired of X - no phrasal verb - extremely common
to tire of X - phrasal verb - not often used

This sentence has both:
I am tired of listening to Mozart's operas, but I never tire of hearing

JigneshbharatiWhat two elements or which two elements?

'which'

There are only a finite number of elements to choose from in that sentence.

which selects.
what identifies.

CJ

One problem here is that there is no general agreement in which verbs followed by a preposition/particle/adverb are phrasal verbs and which are not.

I don't consider 'tire of' to be a phrasal verb. It just happens that 'of' is the preposition that collocates with it. The preposition does not change the meaning of the verb in any way.