To select the sentence with correct punctuation, we must apply grammar and punctuation principles. Let's examine each option:
This sentence contains two errors: "Its" is incorrect and should be "It's" (the contraction of "it is"), and a semicolon is needed instead of a comma to correctly join two independent clauses.
This sentence is punctuated correctly. "It's" is the proper contraction for "it is," and the semicolon accurately separates the two related independent clauses.
This sentence exhibits a contraction error. "Its" requires an apostrophe to become "It's," signifying "it is."
Although "It's" is correct, this sentence is a run-on due to the absence of punctuation between the two independent clauses. A semicolon or a period is necessary.
Consequently, the accurately punctuated sentence is: It's raining; we should take an umbrella.