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Chapter 3: Problem 48

Determine whether each statement makes sense or does not make sense, and explain your reasoning. A conditional statement can never be false if its converse is true.

Short Answer

Expert verified
The provided statement 'A conditional statement can never be false if its converse is true' does not make sense. It is possible for a conditional statement to be false even if its converse is true, as demonstrated through the example.

Step by step solution

01

Understanding the terms

Firstly, it's important to understand what is a conditional statement and its converse. A conditional statement is a statement in the form 'If P then Q'. The converse of the statement is 'If Q then P'.
02

Analyzing the statement

The statement given is 'A conditional statement can never be false if its converse is true'. Now, it's essential to analyze whether this is always true or not.
03

Testing the statement with an example

Let's use an example: 'If it is raining, then the ground is wet (P => Q)'. The converse would be 'If the ground is wet, then it is raining (Q => P)'. The converse can be true, the ground might be wet because it is raining, but the original statement can be false. For example, if the ground is wet not because of rain, but because someone watered the lawn, the conditional statement 'If it is raining, then the ground is wet' is not valid as it's not raining, but the ground is wet. Therefore, it is possible for a conditional statement to be false even if its converse is true.

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Most popular questions from this chapter

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