Thread: 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
For the second statement I got

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?

The first formula should be , 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.

Originally Posted by emakarov

The first formula should be , 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?

Yes, a synonym. It's what is located left of the arrow.