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Chapter 3: Problem 21

Write the converse, inverse, and contrapositive of each statement. If the stereo is playing, then I cannot hear you.

Short Answer

Expert verified
The converse of the statement is 'If I cannot hear you, then the stereo is playing', the inverse is 'If the stereo is not playing, then I can hear you', and the contrapositive is 'If I can hear you, then the stereo is not playing.'

Step by step solution

01

Identify the Hypothesis and Conclusion

The statement is 'If the stereo is playing, then I cannot hear you.' Here, 'the stereo is playing' is the hypothesis and 'I cannot hear you' is the conclusion.
02

Formulate the Converse

The converse of a statement is formed by switching the hypothesis and conclusion of the original statement. Thus for our statement, the converse would be 'If I cannot hear you, then the stereo is playing.'
03

Formulate the Inverse

The inverse of a statement is created by negating both the hypothesis and conclusion of the original statement. So, the inverse of the statement would be 'If the stereo is not playing, then I can hear you.'
04

Formulate the Contrapositive

The contrapositive of a statement is generated by reversing the hypothesis and conclusion of the original statement and also negating them. Therefore, the contrapositive of our statement would be 'If I can hear you, then the stereo is not playing.'

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