# 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.”

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: $\left(P\vee Q\right)\wedge \left(Q\to R\right)\wedge \left(\mathrm{¬}R\to P\right)$
If this is wrong please correct me
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wintern90
Step 1
You're dealing with an argument, rather than a statement, so I would use:
$P\vee Q$
$Q\to R$
$\mathrm{¬}R$
$\therefore P$
If you really insist on a single statement, I would use:
$\left(\left(P\vee Q\right)\wedge \left(Q\to R\right)\wedge \mathrm{¬}R\right)\to P$
This looks like your statement but is crucially different:
Your statement $\left(P\vee Q\right)\wedge \left(Q\to R\right)\wedge \left(\mathrm{¬}R\to P\right)$ can be false simply by setting P and Q to False.
Step 2
My statement $\left(\left(P\vee Q\right)\wedge \left(Q\to R\right)\wedge \mathrm{¬}R\right)\to P$ 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"