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What is the converse of the following conditional statement?

"If this month is September, then next month ends in the letter r."

Determine if the converse is true or false and give a counterexample if the converse is false.

If next month ends in the letter r, then this month is September. The converse is true.
If this month is not September, then next month does not end in the letter r. The converse is true.
If next month ends in the letter r, then this month is September. The converse is false; a counterexample is December.
If this month is not September, then next month does not end in the letter r. The converse is false; a counterexample is December.

1 answer

The original conditional statement is: "If this month is September, then next month ends in the letter r."

The converse of this statement is: "If next month ends in the letter r, then this month is September."

To determine whether the converse is true or false, we consider the months that end in the letter "r" which are October and December:

  1. If this month is August, then next month (September) does not end in "r."
  2. If this month is November, then next month (December) does end in "r."

Since there are scenarios (like November leading to December) where next month ends in "r" but the current month is not September, this indicates that the converse is false.

Counterexample: If this month is November, then next month (December) ends in the letter "r," but this month is not September.

Thus, the correct evaluation is:

  • Converse: "If next month ends in the letter r, then this month is September."
  • Truth Value: False
  • Counterexample: November (leading to December).