Is the word their a preposition?

No, "their" is not a preposition. It is a possessive pronoun, which means it shows ownership or belonging.

Here's why:

* Prepositions show the relationship between a noun or pronoun and another word in the sentence. They often indicate location, time, or direction. Some common prepositions include "on," "in," "under," "to," "from," "with," "by," and "for."

* Possessive pronouns indicate possession. They take the place of a noun phrase that shows ownership. Other possessive pronouns include "my," "your," "his," "her," "its," "our," and "yours."

Example:

* Preposition: The book is on the table. ("On" shows the location of the book.)

* Possessive pronoun: The book is their favorite. ("Their" shows that the book belongs to someone else.)