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Chapter 3: Problem 30

Write the converse, inverse, and contrapositive of each statement. \(\sim p \rightarrow r\)

Short Answer

Expert verified
The converse of the given statement \(\sim p \rightarrow r\) is \(r \rightarrow \sim p\). The inverse of the statement is \(p \rightarrow \sim r\). The contrapositive of the statement is \(\sim r \rightarrow p\).

Step by step solution

01

Converse

To find the converse of the given statement \(\sim p \rightarrow r\), we just swap the hypothesis and the conclusion. So the converse is \(r \rightarrow \sim p\).
02

Inverse

The inverse of a statement is found by negating both the hypothesis and the conclusion of the original statement. For \(\sim p \rightarrow r\), the inverse is therefore \(p \rightarrow \sim r\).
03

Contrapositive

The contrapositive of a statement is found by swapping and negating both the hypothesis and the conclusion. For \(\sim p \rightarrow r\), the contrapositive is therefore \(\sim r \rightarrow p\).

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