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Chapter 1: Problem 15

Give the negation of each statement. Joe did not run in the race.

Short Answer

Expert verified
Joe ran in the race.

Step by step solution

01

- Identify the Original Statement

The original statement is 'Joe did not run in the race.'
02

- Recognize the Negation

To negate a statement, the logical meaning must be reversed. The original statement 'Joe did not run in the race,' needs to be negated.
03

- Formulate the Negation

The negation of the statement 'Joe did not run in the race' is 'Joe ran in the race.' This is because saying that Joe did not do something and then negating it results in Joe doing that thing.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Logical Meaning of Statements
Understanding the logical meaning of a statement is crucial when working with negations. A statement can either be true or false. The logical meaning helps us determine what the statement intends to convey.
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In our exercise, the original statement is: 'Joe did not run in the race.' The logical meaning here is that Joe was not a participant in the race. This needs to be understood before we can proceed to formulate its negation.
Understanding Negation
Negation is the process of reversing the logical meaning of a statement. If a statement is true, its negation is false and vice versa.
To negate a statement, all you have to do is change the truth value of the original statement. Let's take our example. If the statement is: 'Joe did not run in the race,' the negation would involve Joe doing the opposite of not running in the race, which is running in the race.
Negating a statement changes its logical meaning completely. For instance: if the statement is 'The sky is blue,' and we negate it, it becomes 'The sky is not blue.'
Negating the Original Statement
Let's apply the concept of negation to the original statement.
Our original statement is: 'Joe did not run in the race.' To negate it, we reverse its logical meaning.
The reverse of 'Joe did not run' is 'Joe ran.' So, the negation of 'Joe did not run in the race' is 'Joe ran in the race.' It's that simple.
Understanding the original statement and then negating it correctly helps you solve such exercises quickly and accurately.

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