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 identify the correct symbolic form of Jamie's statement about going for a run and not being tired. The statement can be expressed as a conditional statement where if Jamie goes for a run (p), then they will not be tired (¬q). The task is to match this with the given options.

Answer

The correct symbolic form is $ p \rightarrow ¬q $.

Steps to Solve

Understanding the Logic Statement

Identify the main parts of the statement: Jamie says, "If I go for a run (p), then I will not be tired (¬q)."

Identifying Symbolic Forms

We need to express the statement in symbolic logic form. Here, $p$ stands for "I go for a run" and $¬q$ stands for "I am not tired."

Constructing the Conditional Statement

Since Jamie's statement is conditional—if $p$ then $¬q$—we can express it as: $$ p \rightarrow ¬q $$

Matching with Given Options

Now, we compare the derived expression $p \rightarrow ¬q$ with the options provided:

a. $p \rightarrow ¬q$
b. $¬p \rightarrow ¬q$
c. $¬p \rightarrow q$
d. $p \rightarrow q$

Selecting the Correct Option

The correct symbolic form that matches Jamie's statement is option a: $p \rightarrow ¬q$.

The correct symbolic form that matches Jamie's statement is ( p \rightarrow ¬q ).

More Information

This form indicates a conditional relationship where Jamie going for a run prevents tiredness. Understanding symbolic logic is often useful in various fields, such as mathematics and computer science, where conditions and implications are critical.

Tips

Confusing the negation: Make sure you correctly interpret what "not tired" means as ( ¬q ).
Misunderstanding the direction of the implication: Remember that the format “if p, then q” is represented as ( p \rightarrow q ).

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