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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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    https://brainmass.com/math/analytic-geometry/fallacy-converse-428727

    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.

    $2.19