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3. Prove that the conclusion follows from the given premises. 1. VxL(x)→ H(x) 2. L(c) →H(c) 3. 3x-J(x)^L(x) 4.-J(c) ^ L(c) 5. L(c) 6. H(c) 7.-J(c) 8. H(c) ^ J(c) 9. 3xH(x)^J(x) 1. vxL(x) → H(X) 2. L(c) H(c) 3. 3X-J(X) ^L(x) 4. -J(c) ^ L(c) 5. L(c) 6. H(c) 7. -J(c) 8. H(c) -J(c) A 9. 3XH(X) ^-J(x) Steps Simplification from 4 O Modus Ponens 2 and 5 O Premises: VXL(x) → H(X) 3X-J(X)^L(x)) - Conclusion: 3XH(X)^ -J(X) Simplification from 3 O Premise * Reason Existential Universal Existential Generalization Generalization Instantiation Conjunction from 6 and 7 O Universal Instantiation

3. Prove that the conclusion follows from the given premises. 1. VxL(x)→ H(x) 2. L(c) →H(c) 3. 3x-J(x)^L(x) 4.-J(c) ^ L(c) 5. L(c) 6. H(c) 7.-J(c) 8. H(c) ^ J(c) 9. 3xH(x)^J(x) 1. vxL(x) → H(X) 2. L(c) H(c) 3. 3X-J(X) ^L(x) 4. -J(c) ^ L(c) 5. L(c) 6. H(c) 7. -J(c) 8. H(c) -J(c) A 9. 3XH(X) ^-J(x) Steps Simplification from 4 O Modus Ponens 2 and 5 O Premises: VXL(x) → H(X) 3X-J(X)^L(x)) - Conclusion: 3XH(X)^ -J(X) Simplification from 3 O Premise * Reason Existential Universal Existential Generalization Generalization Instantiation Conjunction from 6 and 7 O Universal Instantiation

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 1YT
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3. Prove that the conclusion follows from the given premises. 1. VxL(x) → H(x) 2. L(c) →H(c) 3. 3x-J(x)^L(x) 4.-J(c) ^ L(c) 5. L(C) 6. H(c) 7.-J(c) 8. H(c) ^ -J(c) 9. 3xH(x)^J(x) 1. vxL(x) → H(x) 2. L(c) H(c) 3. 3X¬J(X) ^L(x) 4. -J(c) ^ L(c) 5. L(c) 6. H(c) 7. -J(c) 8. H(c) ^-J(c) 9. 3XH(X) ^ -J(x) Steps Simplification from 4 Modus Ponens 2 and 5 O Premises: VXL(x)→ H(X) 3x¬J(X)^L(x)) Conclusion: 3XH(X)^¬J(X) Simplification from 3 O O O O O Premise O O O O Reason Existential Universal Existential Generalization Generalization Instantiation O о O O O O Conjunction from 6 and 7 Universal Instantiation O O O O
Transcribed Image Text:3. Prove that the conclusion follows from the given premises. 1. VxL(x) → H(x) 2. L(c) →H(c) 3. 3x-J(x)^L(x) 4.-J(c) ^ L(c) 5. L(C) 6. H(c) 7.-J(c) 8. H(c) ^ -J(c) 9. 3xH(x)^J(x) 1. vxL(x) → H(x) 2. L(c) H(c) 3. 3X¬J(X) ^L(x) 4. -J(c) ^ L(c) 5. L(c) 6. H(c) 7. -J(c) 8. H(c) ^-J(c) 9. 3XH(X) ^ -J(x) Steps Simplification from 4 Modus Ponens 2 and 5 O Premises: VXL(x)→ H(X) 3x¬J(X)^L(x)) Conclusion: 3XH(X)^¬J(X) Simplification from 3 O O O O O Premise O O O O Reason Existential Universal Existential Generalization Generalization Instantiation O о O O O O Conjunction from 6 and 7 Universal Instantiation O O O O
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