Which of the following is not true?

Periods and events should be capitalized (i.e. the Great Depression)

Proper nouns must always be capitalized

The days of the week are only capitalized at the beginning of a sentence

The first word of a sentence should always be capitalized (even inside quotation marks)

choose the correct answer

The first word of a sentence should always be capitalized (even inside quotation marks)

Is this answer correct?

Yes, the correct answer is "The first word of a sentence should always be capitalized (even inside quotation marks)" is not true. The first word inside quotation marks should only be capitalized if it is the beginning of a new sentence.