This sentence has a disagreement between a pronoun and its antecedent. The “offer” is singular and “them” is plural. The corrected sentence reads, "Instead of accepting the aliens’ offer to take over, the humans rejected it and attempted vainly to fight back."

The antecedent of the word "them," a plural pronoun, is the word "mom," a singular noun. Pronouns need to match their antecedents' gender and number, so the singular feminine pronoun "her" should be used instead of the plural pronoun "them."

Given that the subject of the sentence is "New York and Los Angeles," which is plural, the pronoun "its" should also be plural. Therefore, "its" should be "their."

"They," a plural pronoun, is used in the sentence to refer to "the mongoose," a singular subject. So, "they" should be changed to "it."

"Their" is a possessive pronoun that indicates that an object belongs to several owners. However, this sentence refers to a single actress, so the lines only belong to one person. Therefore, the best pronoun to use is "her" because it matches the singular nature of the subject: she should study her lines. The correct sentence would be "An actress who struggles with memorization should study her lines daily."

"Their" is a possessive pronoun that indicates that someone belongs to several people. This sentence, however, refers to a single subject (a professor), so the best pronoun to use is one that signifies that an object belongs to one person: in this case, his students. Even though "students" is plural, the plurality of the object does not impact the possessive pronoun. Only the plurality of the subject matters, so "his" is the correct pronoun, making the corrected sentence "A professor who assigns an unreasonable amount of reading for his students may never earn the class's approval."

In this sentence, the pronoun “it” (singular) refers to “witty comebacks” (plural). These words should agree in number. The corrected sentence reads, "Penelope always thought of the most fabulous witty comebacks two hours after the situation in which she could have used them."

In the above sentence, the clause "no merchant should ever be knighted" is being modified by the phrase "no matter how great a difference they made for the country," which means that the pronoun "they" has the antecedent "merchant." Since "merchant" is singular, the pronoun(s) used to replace "merchant" should also be singular—in this case, "he or she."

In this sentence, an error occurs when the possessive plural pronoun "their" is used to refer to a singular masculine antecedent, "Bob." Instead of using the plural possessive pronoun "their," one should use the singular masculine possessive pronoun "his."

The plural pronoun "they" refers back to the subject of the first part of the sentence, "The toucan." Since this noun is singular, the pronoun should be too. Changing "they" to "it" corrects the sentence's error. The corrected sentence reads, "The toucan is primarily recognized by its bright colors; it is painted a mixture of vibrant red, yellow, and blue."