# converting words into logic symbols

• Sep 20th 2011, 06:13 PM
Jskid
converting words into logic symbols
To run a marathon you must be over 5 feet and have a healthy heart. If you are not over 5 feet and do not have a healthy heart, you cannot run the marathon. Right this statement in symbols.

Let a(x) be the assertion "x can run the marathon"
For the first statement I got $\displaystyle (over 5 feet) \wedge (healthy heart) \rightarrow a(x)$
For the second statement I got $\displaystyle \neg (over 5 feet) \wedge \neg (healthy heart) \rightarrow \neg a(x)$

I have a feeling this is wrong because if the hypothesis is false then the statment is true, if I don't use implication what do I use?
• Sep 21st 2011, 03:28 AM
emakarov
Re: converting words into logic symbols
The first formula should be $\displaystyle \forall x\,(\mathop{\mbox{over 5 feet}}(x) \wedge \mathop{\mbox{healthy heart}}(x)\rightarrow a(x))$, and similarly for the second.

The use of implication is correct. These statements are true for all x, including those for whom the premises are false.
• Sep 21st 2011, 12:28 PM
Jskid
Re: converting words into logic symbols
Quote:

Originally Posted by emakarov
The first formula should be $\displaystyle \forall x\,(\mathop{\mbox{over 5 feet}}(x) \wedge \mathop{\mbox{healthy heart}}(x)\rightarrow a(x))$, and similarly for the second.

The use of implication is correct. These statements are true for all x, including those for whom the premises are false.

What does "premises" mean? Is that an synonym for hypothesis?
• Sep 21st 2011, 12:34 PM
emakarov
Re: converting words into logic symbols
Yes, a synonym. It's what is located left of the arrow.