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 \( p \rightarrow ¬q \).
Answer for screen readers
The correct symbolic form that matches Jamie's statement 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 ).
