I am asked to prove that M is true AND P is NOT true.
Prove: M && !P

These are the statements that I am given to solve this riddle:

1. If (J && R) then H (is true)
2. If (R is true then H is true) is true then M is true.
3. !(P || !J)

Here is what I have so far:
Based on number 3, It is not P or not J. Therefore J must be true AND P must be false. I have proven the second part of what I need to prove, that P is false.

To prove that M is true, I need to prove that H is true. To prove that H is true, J and R must be true. J is true, so I need to find a way to prove that R is true. Can anyone solve this riddle?

From 3, J is true, this you know. This means that 1 says: If (True && R) then H, which is the same as: if (R is true then H is true). Now that is the condition in 2 to make M true and finally from 3 you get that P is false. Which you were supposed to prove.

Thanks, but I still don't know how to prove that R is true. I must prove that R is true, to make H true. Once I can prove H true, then M is necessarily true. But how do I prove R is true?

Another way to look at it to prove that Gloin is on the right track is that through formal logic simplification. Since you have proven that J is true that to be in the AND operation with R (a conjunction) R too must be true. Joined by AND you can apply the Simplification rule which states J is true R is True and because of that R being true dictates that H is then true in number 2. Since R is true equals H being true, the line in 2 then proves that M is true.

Another spin on things.

That's very interesting, Martyr2 and Gloin. I'm still not sure if that works, but it is worth a shot.

Yes! I love discrete math!

Knights and Knaves am I right?

Well think of it this way... they give you three statements. They make one of them easy to solve... in this case number 3. This leads to two conclusions, J is true, P is false. Since the other two statements don't use P, you have to assume that you must use J in statement 1 as your next logical step. J being in a conjunct with R is a statement that if J is true then R must be true as well since it is the only way that H can be true and therefore M being true.

Learning Center Smart Tour - Logic - Simplification Rule for conjuncts

That is what I am going by. There is no other way to prove that R is true because no other statements are used to relate to the result of R. So we have to go based strictly on its relationship to J in line 1 and because its relationship with AND.

These logic problems always chain like this. They give you a straight out statement that you must then branch out into the others. The only choice here is to move J up into statement 1 and get its relationship to R.

And yet another way is that if J is true so is R because of the AND Operator and that we apply Modus Ponens to the conjunction so that if it is true then H has to be true...But perhaps that is too far.



This post has been edited by Martyr2: 1 Dec, 2008 - 04:13 PM

I like this problem, it doesn't branch out like other ones can do, the logic is essentially a one way tunnel underground to the answer.

@Martyr2

Thanks a lot! I think this will work.

@KYA
What are you talking about (Knights and Knaves)?

Knights and Knaves