Represent the statement that: “A car is either moving or stationary; if a car is stationary then its brakes are applied; the car does not have its brakes applied therefore the car is moving.”

Nash Frank 2022-07-17 Answered
Represent the statement that: “A car is either moving or stationary; if a car is stationary then its brakes are applied; the car does not have its brakes applied therefore the car is moving.”
I believe i have to use formal logic and connectives while solving this question and i have attempted it but not sure if it is correct. My answer: ( P Q ) ( Q R ) ( ¬ R P )
If this is wrong please correct me
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Answers (1)

wintern90
Answered 2022-07-18 Author has 12 answers
Step 1
You're dealing with an argument, rather than a statement, so I would use:
P Q
Q R
¬ R
P
If you really insist on a single statement, I would use:
( ( P Q ) ( Q R ) ¬ R ) P
This looks like your statement but is crucially different:
Your statement ( P Q ) ( Q R ) ( ¬ R P ) can be false simply by setting P and Q to False.
Step 2
My statement ( ( P Q ) ( Q R ) ¬ R ) P cannot be false, as it is a tautology, as it should, since it corresponds to the argument above, which is valid.
Finally, it is a good habit to make explicit what your symbols stand for:
P: "The car is moving"
Q: "The car is stationary"
R: "The car has its brakes applied"
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