Need help with math homework, its on logic.?
P --> C
P V E
E --> J
C --> H
- mittenLv 51 decade agoFavorite Answer
1. P -> C
2. P v E
3. E --> J
4. C -> H
6. (P ->C) & (E -> J)..1,3, conj
7. C v J..2,6, cd
8. J v C..7, com
9. C..5,8, ds
10. H..4,9, mp
- 1 decade ago
Let's start with one of the statements that is not a conditional statement, since that might be easier. (It might not work, but we'll find out.)
Either ~J or P v E are the non-conditionals that are given, and it is possible to prove H by starting with either. But if starting with one doesn't work, then try the other until you get a proof that does work. You'll have to use all the given statements somehow anyway. I'll start with ~J arbitrarily, and I'll write the proof with words the long way like I would a math proof, since different classes teach different ways of writing logical proofs. I hope it can still be understood.
It is given that ~J. It is also given that E -> J, and the contrapositive of this is (~J -> ~E). Thus, from ~J we conclude that ~E.
However, P v E is given. Since ~E, it must be that P. It is also given that P -> C, so from P we conclude C.
We know that C -> H, and we have just shown C. Therefore, H.
Hence it has been proven that H.