Final answer:
The sentence that uses correct grammar, punctuation, and connecting words is: Many people eliminate meat from their diets, but they don't become strict vegetarians.
Step-by-step explanation:
The correct sentence that uses proper grammar, punctuation, and connecting words is:
Many people eliminate meat from their diets, but they don't become strict vegetarians.
In this sentence, the connecting word 'but' is used correctly to show contrast between two ideas. The sentence is properly punctuated with a comma before 'but'. The subject-verb agreement is also correct.
Learn more about Proper grammar and punctuation in English sentences