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I have a question which i got on my discrete maths coursework and i'm struggling to solve it.

The question is: 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 was: (p v q) ^ (q > r) ^ (-r > p)

If this is wrong please correct me

DarkArmy
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You're dealing with an argument, rather than a statement, so I would use:

$$P \lor Q$$

$$Q \rightarrow R$$

$$\neg R$$

$$\therefore P$$

If you really insist on a single statement, I would use:

$$((P \lor Q) \land (Q \rightarrow R) \land \neg R) \rightarrow P$$

This looks like your statement but is crucially different:

Your statement $(P \lor Q) \land (Q \rightarrow R) \land (\neg R \rightarrow P)$ can be false simply by setting $P$ and $Q$ to False.

My statement $((P \lor Q) \land (Q \rightarrow R) \land \neg R) \rightarrow P$ 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"

Bram28
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  • Thankyou so much for your help, i really do appreciate it. – DarkArmy Oct 16 '17 at 22:03
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    This shows correct ways to write the argument logically; I would just warn that it's possible that this discrete maths course expects another kind of notation. Some people prefer a horizontal line between the premises (everything before the last $P$) and the conclusion ($P$). The only way to know which notation to use really is to find an earlier worked example of an argument (something with the word "therefore") and see how it was converted to symbols. We don't have your textbook in front of us and can't guess the preferences of its author. – David K Oct 16 '17 at 22:04