Correct the following sentences:

They all rejected that idea of the Captain's.

= They all rejected the captain's idea."

This sentence requires correction based on the principle of subject-verb agreement.

The main subject of the sentence is "The basket," which is a singular noun. The phrase "containing ten apples" is a participial phrase acting as an adjective, modifying "basket." It does not alter the number (singularity or plurality) of the main subject.

Since the subject "basket" is singular, the verb must also be singular. The original sentence used "were," which is a plural verb. It should be replaced with the singular past tense verb "was" to agree with the singular subject.

None of us are perfect. = None of us is perfect.

In formal English, the conjunction "as" is used to introduce a clause or a phrase that indicates a comparison or the manner in which something is done. In this sentence, "as in the old days" describes how the evening was spent, implying "in the way it was done in the old days."

Conversely, "like" is primarily used as a preposition to mean "similar to" or "in the manner of," and is typically followed by a noun, pronoun, or noun phrase. While "like" is often used informally in place of "as" or "as if," it is generally considered incorrect in standard written English when introducing a clause or an adverbial phrase of comparison.

For example:

    
• Incorrect: She sings like she is a professional.
    
• Correct: She sings as if she is a professional.
    
• Correct: She sings like a professional. (Here, 'like' is a preposition followed by a noun phrase 'a professional'.)

Therefore, "as in the old days" is the grammatically correct and more formal choice for this context.

In English grammar, 'since' and 'for' are prepositions used to indicate time, particularly with perfect and perfect continuous tenses, but they have distinct uses:

    
• For: Used to express a duration of time. It answers the question "How long?". For example, "for three hours," "for five years," "for two days."
    
• Since: Used to indicate a starting point in time. It answers the question "From when?". For example, "since Monday," "since 2010," "since morning."

In the original sentence, "two days" refers to a duration, not a specific starting point. Therefore, 'for' is the correct preposition to use.

He was accused of a crime he did not commit.