To choose the correctly punctuated sentence, we need to consider both grammar and punctuation rules. Let's analyze the options:
This sentence has two issues: "Its" should be "It's" (a contraction for "it is"), and there should be a semicolon instead of a comma to properly separate two independent clauses.
This sentence is correctly punctuated. "It's" is the correct contraction for "it is," and the semicolon appropriately separates the two related independent clauses.
This sentence has a contraction issue. "Its" should be "It's" to correctly mean "it is."
While "It's" is correct, this sentence lacks punctuation between the two independent clauses, making it a run-on sentence. A semicolon or period is required.
Therefore, the correct sentence is: It's raining; we should take an umbrella.