Consider the natural deduction proof given below. Using your knowledge of the natural deduction proof method and the options provided in the drop- down menus, fill in the blanks to identify the missing information that completes the proof. 1. Kɔ ~K (kכJ כ2J | ~J 3. ~K v ~K Impl 4. 3 ▼ 5. (] • J) ɔ K 6. Jɔ K 7. (Use the following tabs if you need help remembering any of the natural deduction rules you have learned so far.) NATURAL DEDUCTION RULES AND PROOF METHODS Modus Ponens (MP) Modus Tollens (MT) Pure Hypothetical Syllogism (HS) Disjunctive Syllogism (DS) Constructive Dilemma (CD) Simplification (Simp) Conjunction (Conj) Addition (Add) De Morgan's Rule (DM) Commutativity (Com) Associativity (Assoc) Distribution (Dist) Double Negation (DN) Transposition (Trans) Material Implication (Impl) Material Equivalence (Equiv) Exportation (Exp) Tautology (Taut)
Consider the natural deduction proof given below. Using your knowledge of the natural deduction proof method and the options provided in the drop- down menus, fill in the blanks to identify the missing information that completes the proof. 1. Kɔ ~K (kכJ כ2J | ~J 3. ~K v ~K Impl 4. 3 ▼ 5. (] • J) ɔ K 6. Jɔ K 7. (Use the following tabs if you need help remembering any of the natural deduction rules you have learned so far.) NATURAL DEDUCTION RULES AND PROOF METHODS Modus Ponens (MP) Modus Tollens (MT) Pure Hypothetical Syllogism (HS) Disjunctive Syllogism (DS) Constructive Dilemma (CD) Simplification (Simp) Conjunction (Conj) Addition (Add) De Morgan's Rule (DM) Commutativity (Com) Associativity (Assoc) Distribution (Dist) Double Negation (DN) Transposition (Trans) Material Implication (Impl) Material Equivalence (Equiv) Exportation (Exp) Tautology (Taut)
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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![Consider the natural deduction proof given below. Using your knowledge of the natural deduction proof method and the options provided in the drop-
down menus, fill in the blanks to identify the missing information that completes the proof.
1.
Kɔ ~K
2.
(K כ J כנ
| ~]
3.
~K V NK
1
Impl
4.
~K
3
5.
(J • J) ɔ K
6.
K כנ
7.
~J
(Use the following tabs if you need help remembering any of the natural deduction rules you have learned so far.)
NATURAL DEDUCTION RULES AND PROOF METHODS
Modus Ponens (MP)
Modus Tollens (MT)
Pure Hypothetical Syllogism (HS)
Disjunctive Syllogism (DS)
Constructive Dilemma (CD)
Simplification (Simp)
Conjunction (Conj)
Addition (Add)
De Morgan's Rule (DM)
Commutativity (Com)
Associativity (Assoc)
Distribution (Dist)
Double Negation (DN)
Transposition (Trans)
Material Implication (Impl)
Material Equivalence (Equiv)
Exportation (Exp)
Tautology (Taut)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ef063f0-0adf-43ac-9c0c-651ac0fbbf37%2Fd2eb4881-ac87-45ba-947e-ec28233bf762%2Febqu8yi_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the natural deduction proof given below. Using your knowledge of the natural deduction proof method and the options provided in the drop-
down menus, fill in the blanks to identify the missing information that completes the proof.
1.
Kɔ ~K
2.
(K כ J כנ
| ~]
3.
~K V NK
1
Impl
4.
~K
3
5.
(J • J) ɔ K
6.
K כנ
7.
~J
(Use the following tabs if you need help remembering any of the natural deduction rules you have learned so far.)
NATURAL DEDUCTION RULES AND PROOF METHODS
Modus Ponens (MP)
Modus Tollens (MT)
Pure Hypothetical Syllogism (HS)
Disjunctive Syllogism (DS)
Constructive Dilemma (CD)
Simplification (Simp)
Conjunction (Conj)
Addition (Add)
De Morgan's Rule (DM)
Commutativity (Com)
Associativity (Assoc)
Distribution (Dist)
Double Negation (DN)
Transposition (Trans)
Material Implication (Impl)
Material Equivalence (Equiv)
Exportation (Exp)
Tautology (Taut)
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