Jamie decides, 'If I go for a run, then I will not be tired.' If p: 'I go for a run' and q: 'I am tired,' which symbolic form matches Jamie's statement?
Understand the Problem
The question is asking to translate a conditional statement made by Jamie into symbolic logic. Specifically, it seeks the correct expression for the statement 'If I go for a run, then I will not be tired,' using the provided symbols for 'I go for a run' and 'I am tired.'
Answer
The symbolic form is \( p \rightarrow \neg q \).
Answer for screen readers
The correct symbolic form is ( p \rightarrow \neg q ).
Steps to Solve
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Identify the Components of the Statement
The statement "If I go for a run, then I will not be tired" can be broken down.
- Let ( p ) represent "I go for a run".
- Let ( q ) represent "I am tired".
The phrase "I will not be tired" implies the negation of ( q ), expressed as ( \neg q ).
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Set Up the Conditional Statement
In logic, the structure "If p, then q" is represented as ( p \rightarrow q ).
In this case, Jamie's statement translates to:
$$ p \rightarrow \neg q $$ -
Select the Correct Symbolic Form
From the options provided: -
( \neg p \rightarrow \neg q )
-
( p \rightarrow \neg q )
-
( \neg p \rightarrow q )
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( p \rightarrow q )
We see that the correct symbolic form is the second option, ( p \rightarrow \neg q ).
The correct symbolic form is ( p \rightarrow \neg q ).
More Information
This logical statement illustrates a conditional relationship where performing one action (going for a run) results in the non-occurrence of another (not being tired). Understanding how to translate spoken language into symbolic logic is a foundational skill in both mathematics and philosophy.
Tips
- Confusing the negation of ( q ) with ( q ) itself. Remember that "not tired" is ( \neg q ), not ( q ).
- Misplacing the order of the conditional statement. Ensure that "If p then q" follows the correct structure.
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