Question

What is the converse of the following conditional statement?

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

Determine the validity of the converse and give a counterexample if the converse is not valid.

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

Answer 1

@joe348

Answer 2

@questioncovebot

Answer 3

@jhonyy9

Answer 4

Which one do you think it is?

Answer 5

im thinking c but idk if the counterexample makes sense

Answer 6

You’ve correctly identified the converse by switching the if/then statements.

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

This sentence implies that, if the next month ends in r, then this month must be September. This is invalid. This month could be October or November, because the month after October ends in r, and the month after November also ends in r.

So yes, C is correct. The converse is invalid.

Answer 7

THANK YOU!