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Chapter 3: Problem 23

Write the converse, inverse, and contrapositive of each statement. "If you don't laugh, you die." (humorist Alan King)

Short Answer

Expert verified
The converse of the statement is 'If you die, then you didn't laugh.' The inverse is 'If you do laugh, then you don't die.' The contrapositive is 'If you don't die, then you did laugh.'

Step by step solution

01

Identify the hypothesis and conclusion

Identify the hypothesis (p) and conclusion (q) in the given statement. For 'If you don't laugh, you die', the hypothesis, or p, is 'You don't laugh', and the conclusion, or q, is 'You die'.
02

Formulate the converse statement

Swap the hypothesis and conclusion to form the converse from the original statement. The converse of 'If you don't laugh, you die' becomes 'If you die, then you didn't laugh.'
03

Formulate the inverse statement

Negate both the hypothesis and conclusion to form the inverse from the original statement. The inverse of 'If you don't laugh, you die' becomes 'If you do laugh, then you don't die.'
04

Formulate the contrapositive statement

Swap and negate both the hypothesis and conclusion to form the contrapositive from the original statement. The contrapositive of 'If you don't laugh, you die' therefore becomes 'If you don't die, then you did laugh.'

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Most popular questions from this chapter

If you are given an argument in words that contains two premises and a conclusion, describe how to determine if the argument is valid or invalid.

Use Euler diagrams to determine whether each argument is valid or invalid. All cowboys live on ranches. All cowherders live on ranches. Therefore, all cowboys are cowherders.

Use Euler diagrams to determine whether each argument is valid or invalid. All comedians are funny people. Some funny people are professors. Therefore, some comedians are professors.

Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument's symbolic form to a standard valid or invalid form. (You can ignore differences in past, present, and future tense.) If an argument is in the form of the fallacy of the inverse, then it is invalid. This argument is invalid. \(\therefore\) This argument is in the form of the fallacy of the inverse.

Write an example of an argument with two quantified premises that is invalid but that has a true conclusion.
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