Which of these sentences use semicolons correctly?

The sentence that uses semicolons correctly is the one stating, "They were at lunch; meanwhile we were working hard." Semicolons are used to connect two independent clauses that are closely related yet could stand alone as separate sentences. In this case, "They were at lunch" and "we were working hard" are both independent clauses. The semicolon effectively indicates a pause that maintains the connection between the two thoughts while allowing for a shift in focus introduced by "meanwhile."

The other options either misuse semicolons or employ punctuation incorrectly. For instance, in the option that says, "He went shopping; and bought groceries," the phrase "and bought groceries" is dependent on the first clause; it doesn't stand alone as a complete thought, making the semicolon inappropriate.

In the sentence that states, "It grew dark outside - the game was still on," the dash is misused here. A semicolon would have been more suitable to link the two independent ideas naturally.

Lastly, in "She was tired: she went to bed early," the colon is incorrectly used since what follows is not a list or a clarification of the first clause. A semicolon would work better here, as both parts of the sentence are independent and