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Name: Date: Introduction to Formal Logic – Natural Deduction Examination – Spring 2014 Part I: True/False Instructions. Please circle ‘True ‘if the statement is true and ‘False’ if the statement is...

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Name:    Date:
Introduction to Formal Logic – Natural Deduction Examination – Spring 2014
Part I: True/False
Instructions. Please circle ‘True ‘if the statement is true and ‘False’ if the statement is false. (2 pts each)
1. The function of the rules of inference is to justify the steps of a proof.
A) True        B) False
2. A proof is a sequence of steps in which each step is either a premise or follows from earlier steps in the sequence according to the rules of inference.
A) True        B) False
3. Implication rules can be validly applied to part of a line.
A) True        B) False
4. According to the axiom of replacement, logically equivalent expressions may replace each other within the context of a proof.
A) True        B) False
5. Replacement rules are pairs of logically equivalent statement forms.
A) True        B) False
6. Conditional proof (CP) is a method that starts by assuming the negation of the required statement and then validly deriving a contradiction on a subsequent line.
A) True        B) False
7. Indirect proof (IP) is a method that starts by assuming the antecedent of a conditional statement on a separate line and then proceeds to validly derive the consequent on a separate line.
A) True        B) False
8. Invalid arguments cannot be proven as invalid using the methods of natural deduction.
A) True        B) False
9. One of the rules of inference is DeMorgan’s theorem: ~(P v Q) :: (~P · ~ Q)
A) True        B) False
10. When an indirect proof is discharged, any lines derived from the assumption can no longer be used in the subsequent proof.
A) True        B) False
Part II: Rules of Implication
Instructions. Using the rules of implication, please provide the proofs for the following problems. Please provide justifications for each step. (7 pts each)
11.         1.     T ( P v Q )
        2.     S v ~ ( P v Q )
        3.     ~S     / ~ T
12.         1.     ( S R ) · Q
        2.     R T     / S T
13.         1.     [ ( T · R ) v S ] ( P v Q )
        2.     T
        3.     R     / P v Q
14.          1. P v ( T v R )
         2. T S
         3. R Q
         4. ~ P     / S v Q
Part II: Rules of Replacement
Instructions. Using the rules of implication and replacement, please provide the proofs for the following problems. Please provide justifications for each step. (7 pts each)
15.          1.     G · K
         2.     K E
         3.     E ( G H )         / H
16.          1. M v ( D · L)
         2. B ~ ( M v L ) / ~ B
17.             1. ~ ( R · R )      / R ⊃ Q
18.             1. T v S
             2. ~ T
            3. ( S v S ) ( ~ P v R )     / ~ R ~ P
Part III: Conditional Proof
Instructions. Please use a conditional proof to solve the following problem. (7 pts)
19.             1.     (D v E) (F · G)
        2.     ( A v B) (D · C)     / A F
Part IV: Indirect Proof
Instructions. Please use an indirect proof to solve the following problem. (7 pts)
20.         1.     B (C ~ B)
        2.     A ( B C)     / ~ A v ~ B
Answered Same Day Apr 13, 2020

Solution

Vidhi answered on Apr 15 2020
134 Votes
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Order ID: 29355
Subject: Computer Science » Design and Analysis of Algorithms
Introduction to Formal Logic – Natural Deduction Examination – Spring 2014
Part I: True/False
Instructions. Please circle ‘True ‘if the statement is true and ‘False’
if the statement is false. (2 pts each)
1. The function of the rules of inference is to justify the steps of a proof.
A) True
2. A proof is a sequence of steps in which each step is either a
premise or follows from earlier steps in the sequence
according to the rules of inference.
A) True
3. Implication rules can be validly applied to part of a line.
B) False
4. According to the axiom of replacement, logically equivalent expressions may replace each other
within the context of a proof.
B) False
5. Replacement rules are pairs of logically equivalent statement forms.
A) True
6. Conditional proof (CP) is a method that starts by assuming the negation of the required statement and then validly deriving a contradiction on a subsequent line.
A) True
7. Indirect proof (IP) is a method that starts by assuming the antecedent of a conditional statement on a separate line and then proceeds to validly derive the consequent on a separate line.
A) True
8. Invalid arguments cannot be proven as invalid using the methods
of natural deduction.
A) True
9. One of the rules of inference is DeMorgan’s theorem: ~(P v Q) :: (~P · ~ Q)
A) True
10. When an indirect proof is discharged,
any lines derived from the assumption
can no longer be used in the subsequent proof.
B) False
Part II: Rules of Implication
Instructions. Using the rules of implication, please provide the proofs for the following problems.
Please provide justifications for each step. (7 pts each)
11. 1. TÉ( P v Q )
2. Sv ~ ( P v Q )
3. ~S / ~T
Answer :-
        S
        T
        ~S/~T
        T
        T
        T
        T
        F
        F
        F
        T
        F
        F
        F
        T
12. 1. ( SÉR )...
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