English - rfvv, Monday, March 16, 2015 at 11:17pm

1. I am good at playing the piano.
2. I am good at the piano.
3. I am good at playing basketball.
4. I am good at basketball.
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Are they all grammatical?

Yes, they are. The sentences "at playing..." are better because they are more specific. "...at the piano" and "at basketball" are more colloquial, but are correct.

To determine if the given sentences are grammatical, we need to analyze their structure and word usage.

1. "I am good at playing the piano." - This sentence is grammatically correct. It consists of the subject pronoun "I," the linking verb "am," the adjective "good," the preposition "at," and the gerund phrase "playing the piano."

2. "I am good at the piano." - This sentence is also grammatically correct. It follows a similar structure as sentence 1 but omits the word "playing." In this case, "piano" is used as a noun, and the prepositional phrase "at the piano" indicates where the person shows their skill.

3. "I am good at playing basketball." - This sentence is grammatically correct as well. It has the same structure as sentence 1, but it replaces "the piano" with "basketball," indicating the activity in which the person excels.

4. "I am good at basketball." - This sentence is grammatically correct too. It follows the structure of sentence 2, using "basketball" as a noun rather than a gerund phrase.

In conclusion, all of the given sentences are grammatically correct, as they follow standard English sentence structure and word usage.