document.write( "Question 1031311: 1. ∀x(~(Fx v Gx) -> Hx)
\n" ); document.write( "2. ∀x(Hx -> Lx)
\n" ); document.write( "3. ∀x(~Fx) Conclusion: ∀x(Gx v Lx)\r
\n" ); document.write( "\n" ); document.write( "Could you solve this using the quantifier rules, identity rules, eight rules of inference and ten equivalence rules please? \n" ); document.write( "

Algebra.Com's Answer #646637 by robertb(5830) $\"\"$ $\"About$

You can put this solution on YOUR website!
1. ∀x(~(Fx v Gx) -> Hx) ----------Hypothesis
\n" ); document.write( "2. ~(Fx v Gx) -> Hx ------------------Universal instantiation
\n" ); document.write( "3. ∀x(Hx -> Lx) ---- ----------------Hypo.
\n" ); document.write( "4. Hx -> Lx -------------------------Universal instantiation
\n" ); document.write( "5. ~(Fx v Gx) -> Lx -------------------Hypothetical syllogism on #2 and #4
\n" ); document.write( "6. (~Fx∩~Gx) -> Lx ------------------- de Morgan's law
\n" ); document.write( "7. ~Fx -> (~Gx-> Lx) ---------------- Exportation
\n" ); document.write( "8. ∀x(~Fx) ---------------------------Hypo.
\n" ); document.write( "9. ~Fx -----------------------Universal instantiation
\n" ); document.write( "10. ~Gx-> Lx -------------------------Modus ponens on #7 and #9
\n" ); document.write( "11. ~~Gx v Lx -------------------------Material implication
\n" ); document.write( "12. Gx v Lx ---------------------------Double negation
\n" ); document.write( "13. ∀x(Gx v Lx) -----------------------Universal generalization \n" ); document.write( "

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