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.Com
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) (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
RELATED QUESTIONS
Can you help me construct a proof for these arguments? Thanks in advance.
1.
(x)((Fx &... (answered by richwmiller)
Complete the following derivation: --THANK YOU!! THIS IS MUCH NEEDED
1. ~[∀x:... (answered by addingup)
fx-gx=h solve the equation for... (answered by tommyt3rd)
Solve for x by completing the square:... (answered by stanbon)
Prove or give a counterexample to each statement.
∀x ∈ ℝ, ((x^2) +... (answered by jim_thompson5910)
Let fx= x-5 and gx=x^2-1. Find each of the following functions.
A.... (answered by Fombitz)
f(x)+g(x)
fx = 3x+5
gx =... (answered by MathLover1)
I need to help on the following proofs
Proof 1
B ∧ F
¬(B ∧ G)... (answered by Edwin McCravy)
I need help help help
∀x, u ∈ R ∃α,β ∈ [0, 1] such (answered by tommyt3rd)