Final answer:
The converse of the statement switches the hypothesis and conclusion, and in the provided example, the converse is false due to counterexamples such as the months of November and December.
Step-by-step explanation:
The converse of a conditional statement switches the hypothesis and the conclusion. For the statement "If this month is September, then next month ends in the letter r," the converse would be: "If next month ends in the letter r, then this month is September." To determine if the converse is true, we need to consider if there could be a month ending with the letter "r" that does not follow September. October, November, and December all end in "r" and October follows September. However, November and December do not follow September but still end in "r," so these are counterexamples that demonstrate the converse is false.