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Chapter 3: Problem 24

Write the converse, inverse, and contrapositive of each statement. "If it doesn't fit, you must acquit." (lawyer Johnnie Cochran)

Short Answer

Expert verified
The converse of the statement is: 'If you must acquit, then it doesn't fit.' The inverse is: 'If it fits, then you must not acquit.' And the contrapositive is: 'If you don't acquit, then it fits.'

Step by step solution

01

Identifying the original statement.

The original statement is an 'if-then' statement: 'If it doesn't fit, you must acquit.' Here, 'it doesn't fit' is the condition (P), and 'you must acquit' is the result or consequence (Q). The statement can be symbolically represented as 'If P, then Q.'
02

Constructing the converse.

The converse of a statement switches the roles of the condition and the consequence. That is, if the original statement is 'If P, then Q,' its converse would be 'If Q, then P.' Therefore, the converse of the original statement is: 'If you must acquit, then it doesn't fit.'
03

Constructing the inverse.

The inverse of a statement negates both the condition and the consequence. If the original statement is 'If P, then Q,' its inverse would be 'If not P, then not Q.' Thus, the inverse of the original statement is: 'If it fits, then you must not acquit.'
04

Constructing the contrapositive.

The contrapositive switches the roles of the condition and the consequence and then negates both. If the original statement is 'If P, then Q,' its contrapositive would be 'If not Q, then not P.' As a result, the contrapositive of our original statement is: 'If you don't acquit, then it fits.'

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Most popular questions from this chapter

Write a valid argument on one of the following questions. If you can, write valid arguments on both sides. a. Should the death penalty be abolished? b. Should Roe v. Wade be overturned? c. Are online classes a good idea? d. Should marijuana be legalized? e. Should grades be abolished? f. Should same-sex marriage be legalized?

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 I am at the beach, then I swim in the ocean. If I swim in the ocean, then I feel refreshed. \(\therefore\) If I am at the beach, then I feel refreshed.

Use a truth table to determine whether the symbolic form of the argument is valid or invalid. $$ \begin{aligned} &p \rightarrow q \\ &\frac{q \rightarrow p}{\therefore p \wedge q} \end{aligned} $$

In Exercises 51-58, translate each argument into symbolic form. Then determine whether the argument is valid or invalid. If it was any of your business, I would have invited you. It is not, and so I did not.

Use the standard forms of valid arguments to draw a valid conclusion from the given premises. If I vacation in Paris, I eat French pastries. If I eat French pastries, I gain weight. Therefore, ...
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