SOLUTION: 1. ∀x(~(Fx v Gx) -> Hx) 2. ∀x(Hx -> Lx) 3. ∀x(~Fx) Conclusion: ∀x(Gx v Lx) Could you solve this using the quantifier rules, identity rules, eight r

Algebra ->  Proofs -> SOLUTION: 1. ∀x(~(Fx v Gx) -> Hx) 2. ∀x(Hx -> Lx) 3. ∀x(~Fx) Conclusion: ∀x(Gx v Lx) Could you solve this using the quantifier rules, identity rules, eight r      Log On


   

Question 1031311: 1. ∀x(~(Fx v Gx) -> Hx)
2. ∀x(Hx -> Lx)
3. ∀x(~Fx) Conclusion: ∀x(Gx v Lx)
Could you solve this using the quantifier rules, identity rules, eight rules of inference and ten equivalence rules please?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
1. ∀x(~(Fx v Gx) -> Hx) ----------Hypothesis
2. ~(Fx v Gx) -> Hx ------------------Universal instantiation
3. ∀x(Hx -> Lx) ---- ----------------Hypo.
4. Hx -> Lx -------------------------Universal instantiation
5. ~(Fx v Gx) -> Lx -------------------Hypothetical syllogism on #2 and #4
6. (~Fx∩~Gx) -> Lx ------------------- de Morgan's law
7. ~Fx -> (~Gx-> Lx) ---------------- Exportation
8. ∀x(~Fx) ---------------------------Hypo.
9. ~Fx -----------------------Universal instantiation
10. ~Gx-> Lx -------------------------Modus ponens on #7 and #9
11. ~~Gx v Lx -------------------------Material implication
12. Gx v Lx ---------------------------Double negation
13. ∀x(Gx v Lx) -----------------------Universal generalization