# Four predicate logic proofs

I am looking for help with Predicate and Quantitative Logic.
Provide proofs for the attached 4 problems using the 9 rules of inference, the 10 rules of replacement and Quantitative logic.

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Provide proof s for the following four arguments using:

The 9 rules of inference; Modus Pollens (MP); Modus Tollens (MT); Hypothetical Syllogism (HS);
Disjunctive Syllogism (DS); Constructive Dilemna (CD); Absorption (Abs); Simplification (Simp);

The 10 rules of replacement: DeMorgans Theorems (DeM); Commutation (Com); Association (Assoc);
Distribution (Dist);Double Negation (DN); Transposition (Trans); Implication (Impl);
Equivalence (Equiv); Exportation (Exp); and Repetition (Rep)

Quantification Logic: Universal Instantiation (UI); Universal Generalization (UG); Existential
Generalization (EG); Existential Instantiation (EI) and Change of Quantifier Rules (CQ)

1)
1. (x) [Ax > Bx > Cx)]
2. (3x) (Ax v Dx)
3. (x) ~Dx
4. (x) Bx / (3x) Cx

2)
1. ~(3x) (Ax & ~Bx)
2. ~(3x) (Bx & ~Cx) / (x) (Ax > Cx)

3)
1. (3x) (~Hx) > (x) (Ax > Bx)
2. ~(x) (Hx v Bx) / (3x) ~Ax

4)
1. (3x) (Px v Gx) > (x) Hx
2. (3x) (~Hx) / (x) (~Px)
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This question has the following supporting file(s):

• Final Exam Problems.doc
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Solution Summary

Provides completed proofs for four predicate / quantitative logic proofs.

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• Quantificational Proofs 79871.doc

Extracted Content from Question Files:

• Final Exam Problems.doc

Provide proof s for the following four arguments using:

The 9 rules of inference; Modus Pollens (MP); Modus Tollens (MT); Hypothetical Syllogism (HS);
Disjunctive Syllogism (DS); Constructive Dilemna (CD); Absorption (Abs); Simplification (Simp);

The 10 rules of replacement: DeMorgans Theorems (DeM); Commutation (Com); Association (Assoc);
Distribution (Dist);Double Negation (DN); Transposition (Trans); Implication (Impl);
Equivalence (Equiv); Exportation (Exp); and Repetition (Rep)

Quantification Logic: Universal Instantiation (UI); Universal Generalization (UG); Existential
Generalization (EG); Existential Instantiation (EI) and Change of Quantifier Rules (CQ)

1)
1. (x) [Ax > Bx > Cx)]
2. (3x) (Ax v Dx)
3. (x) ~Dx
4. (x) Bx / (3x) Cx

2)
1. ~(3x) (Ax & ~Bx)
2. ~(3x) (Bx & ~Cx) / (x) (Ax > Cx)

3)
1. (3x) (~Hx) > (x) (Ax > Bx)
2. ~(x) (Hx v Bx) / (3x) ~Ax

4)
1. (3x) (Px v Gx) > (x) Hx
2. (3x) (~Hx) / (x) (~Px)