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Rules of inference

Eluki

New member
Dec 6, 2019
1
Hi,

I am havinga bit of challenge with the following question.
What seems confusing to me is th relationship between hypothesis 1 and 2.
I will appreciate all help.


WhatsApp Image 2019-12-06 at 22.18.24.jpeg
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,485
Welcome to the forum.

I am having a bit of challenge with the following question.
It would help if you write exactly what the problem is asking you to do. And I mean as precisely as possible: saying "Prove that the hypotheses imply the conclusion" is not precise enough because the word "imply" can have several different meanings in mathematical logic.

What seems confusing to me is the relationship between hypothesis 1 and 2.
Would you be puzzled if I said that I find confusing the relationship between the following statements: "All my pets are dogs or cats" and "If a pet is a cat, it is a feline"? I suspect you would because it is not even clear what I mean by a relationship: these are two separate statements, nobody claims that they have to be consistent, or follow from each other, or anything like that. What relationship did you find or want to find between hypotheses 1 and 2, and why is this relationship confusing?
 

Alan

Member
Jul 21, 2012
58
Here's a proof (fill out the details).
1. Ax (Px v Qx)
2. Ax (~Qx v Sx)
3. Ax (Rx ->~Sx)
4. Ex ~Px
5. Pa v Qa , universal, 1.
6. ~Qa v Sa universal, 2.
7. Ra ->~Sa , universal, 3.
8. ~Pb, existential, 4.
9.Qb ,5,8 DS.
10. ~~Qb, 9, DN.
11. Sb 7,6, DS.
12. ~~Sb ->~Rb 7, MT.
13. ~Rb , 11,12, MP.
14. Ex ~Rx, QED.