Which of the following sentences properly uses a gerund?

I am celebrating my birthday at Miss Rachel's Pantry.
Miss Rachel's Pantry is a popular restaurant for celebrating special occasions.
Miss Rachel's Pantry is a popular restaurant to celebrate special occasions.
Miss Rachel's Pantry is the restaurant where I celebrated my birthday last year.

Miss Rachel's Pantry is a popular restaurant for celebrating special occasions.

The sentence that properly uses a gerund is:

"Miss Rachel's Pantry is a popular restaurant for celebrating special occasions."

To determine which of the following sentences properly uses a gerund, let's first understand what a gerund is.

A gerund is a verb form that ends in -ing and functions as a noun in a sentence. It is created by adding -ing to the base form of a verb. Gerunds can act as subjects, objects, or complements in a sentence.

Now let's analyze each sentence to identify the proper usage of a gerund:

1. "I am celebrating my birthday at Miss Rachel's Pantry."
In this sentence, "celebrating" is the gerund because it functions as the main verb and as the activity being performed. It acts as a noun, representing the action of celebrating and serving as the object of the verb "am."

2. "Miss Rachel's Pantry is a popular restaurant for celebrating special occasions."
In this sentence, "celebrating" is also the gerund. It acts as the object of the preposition "for" and represents the purpose or reason for which the restaurant is popular.

3. "Miss Rachel's Pantry is a popular restaurant to celebrate special occasions."
In this sentence, "to celebrate" is not a gerund. It is an infinitive phrase where "to" is used as part of the infinitive verb "celebrate." Infinitives, unlike gerunds, are verb forms that function as nouns, adjectives, or adverbs.

4. "Miss Rachel's Pantry is the restaurant where I celebrated my birthday last year."
In this sentence, "celebrated" is not a gerund either. It is a simple past tense verb that functions as the main verb of the relative clause modifying "restaurant."

Therefore, the sentence that properly uses a gerund is:

2. "Miss Rachel's Pantry is a popular restaurant for celebrating special occasions."