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fallacy of the Converse

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Identify which argument is invalid.

If I sing in the shower, then I will not be overheard while singing.
I sang in the shower.
Therefore, I was not overheard while singing.

Either I sing in the shower or I will be overheard while singing.
I did not sing in the shower.
Therefore, I was overheard while singing.

If Sally is on vacation, then Tom is at work.
Tom is not at work.
Therefore, Sally is not on vacation.

If Sally is on vacation, then Tom is at work.
Tom is at work.
Therefore, Sally is on vacation.

If I shower in the morning, then I do not smell bad.
I do not smell bad, then I smile a lot.
Therefore, if I shower in the morning, then I smile a lot.

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Solution Preview

The fourth argument is invalid by Fallacy of the Converse

If Sally is on vacation, then Tom is at work.
Tom is at work.
Therefore, Sally is on vacation.

Here are the detailed explanations:

Let P="I sing in the shower"
Q="I am overheard singing"

The ...

Solution Summary

Law of Syllogism is also applied to the arguments.

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Fallacies are everywhere. They can be so common that they hide from even the savviest reader. Ideally, now that you've familiarized yourself with the common fallacy types, you will be able to think of applications in your own life. For this log, reflect upon a recent encounter you had - this could be with a person, a text, or a piece of media. Did you encounter any fallacies? If you believe that you might have, but you can't assign a specific name to the behavior that you witnessed, do your best to describe what went wrong. If these common fallacies don't quite fit, the exercise of finding fallacious logic still has merit.

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