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.

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facundo3141592 facundo3141592 · Answer 1 · 2022-08-17T17:29:16+02:00

the converse of our statement is:

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

And we prove that is false by finding a counterexample (current month is August is a counterexample).

We have the conditional statement:

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

Remember that for a conditional statement:

"if P then Q"

The converse is:

"If Q then P"

So the converse of our statement is:

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

Now we need to check the validity of this statement. Which clearly is false.

Because September ends with an r, then you can be in August and the next month will end with an r, but the current month will not be September.

That is the counterexample for the converse statement.

If you want to learn more about counterexamples:

https://brainly.com/question/88496

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