Final answer:
The corrected sentence should be: "It's not my book, so it must be yours or hers." The apostrophe in "It's" is used to form a contraction for "it is," indicating that the book belongs to someone else, and no apostrophe is needed for the possessive pronouns "yours" and "hers."
Step-by-step explanation:
The sentence in question requires the appropriate use of apostrophes to show possession and to form contractions correctly. The corrected punctuation would be: "It's not my book, so it must be yours or hers." Here, "It's" is a contraction of "it is," indicating that the book does not belong to the speaker.
The possessive pronouns "yours" and "hers" do not require apostrophes, as possessive personal pronouns already show ownership without them.
Remember, correct punctuation is crucial for clarity. When unsure about whether to use "its" or "it's," simply expand "it's" to "it is" or "it has." If the sentence makes sense with the expanded form, then the correct choice is "it's." If not, then "its" should be used. As an example, "The dog wagged its tail" is correct, as "it is" would not make sense in this context.