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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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