1. The letter on the table is yours.

2. A letter on the table is yours.
[#1 is correct? What about #2?]

3. He kept singing the song.
[In this sentence, what is the part of speech of 'kept'? Is 'kept' a transitive verb? And is 'singing' the object of the verb? Or is 'kept' an intransitive verb? And is 'singing' the subject complement of the verb?]

#1 indicates one letter on the table. #2 indicates one of more than one letter is on the table, but only one of them is yours.

#3. "kept" is a transitive verb. Something must be maintained, singing (crying, shouting, whatever he's doing) or an object, whatever, so it takes a direct object. In this case, singing is being maintained or kept. To keep doing something or to keep an object is an action.

1. Both sentence #1 and sentence #2 can be correct, depending on the context. In sentence #1, "The letter on the table is yours," suggests that there is a specific letter on the table that belongs to you. "The" indicates a definite article, implying a specific letter. In sentence #2, "A letter on the table is yours," suggests that there are multiple letters on the table, and one of them belongs to you. "A" is an indefinite article, indicating that the letter is not specific or known. Both sentences can be valid depending on the intended meaning.

2. In sentence #3, "He kept singing the song," the word "kept" functions as a transitive verb. A transitive verb is a verb that requires an object to complete its meaning. In this sentence, "singing the song" is the object of the verb "kept." The action of "kept" is being applied to the activity of singing the song. Therefore, "kept" is transitive.

Regarding the role of "singing" in the sentence, it is not the direct object or the subject complement. Instead, "singing" is a gerund acting as a noun. It functions as the object of the verb "kept." The entire phrase "singing the song" serves as the direct object of the verb "kept."