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Chapter 3: Problem 20

Write the converse, inverse, and contrapositive of each statement. If I am in Birmingham, then I am in the South.

Short Answer

Expert verified
The converse of the statement is 'If I am in the South, then I am in Birmingham'. The inverse is 'If I am not in Birmingham, then I am not in the South'. The contrapositive is 'If I am not in the South, then I am not in Birmingham'.

Step by step solution

01

Identify p and q

First, identify 'p' and 'q' from the original statement 'If I am in Birmingham, then I am in the South'. In this case, 'I am in Birmingham' is 'p' and 'I am in the South' is 'q'.
02

Write the Converse

Write the converse of the statement by interchanging 'p' and 'q'. So the converse of the statement is 'If I am in the South, then I am in Birmingham'.
03

Write the Inverse

Next, write the inverse of the statement by negating both 'p' and 'q'. The inverse of the statement is 'If I am not in Birmingham, then I am not in the South'.
04

Write the Contrapositive

Finally, write the contrapositive of the statement by interchanging and negating both 'p' and 'q'. The contrapositive of the statement is 'If I am not in the South, then I am not in Birmingham'.

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