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Answered Same DayOct 14, 2021

Solution

Yasodharan answered on Oct 15 2021
56 Votes
Description
    
    Instructions
    Questions 1-6. Identify the substitution instances of the nine rules of inference.
Questions 7-10.  Specify the rule that was used to derive the line specified in each question.
Questions 11-13. Choose the best translation for each sentence
Question 14 and 15. Calculate the truth value of these sentences using the truth conditions of the connectives.
Questions 16 and 17. Do a truth table and specify whether the argument is valid or invalid
Questions 18-20. Complete a proof for each argument.
    Multiple Attempts
    Not allowed. This test can only be taken once.
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Question 1
1. (P • ∼Q) ⊃ (S ⊃ ∼T)
 ~(S ⊃ ∼T)
∴ ~(P • ∼Q)
    
    a.
    Modus Ponens (MP)
    
    b.
    Modus Tollens (MT)
    
    c.
    Simplification (Simp)
    
    d.
    Disjunctive Syllogism (DS)
    
    e.
    None of the above
5 points
Question 2
1. [(P  Q) (P Q)]
 [(P  Q) (P Q)] R
    
    a.
    Conjunction (Conj)
    
    b.
    Simplification (Simp)
    
    c.
    Addition (Add)
    
    d.
    Absorption (Abs)
    
    e.
     None of the above
5 points
Question 3
1. (P Q) (R  S)
(P Q) [(P Q) (R  S)]
    
    a.
    Conjunction (Conj)
    
    b.
    Simplification (Simp)
    
    c.
    Addition (Add)
    
    d.
    Absorption (Abs)
    
    e.
    None of the above
5 points
Question 4
1. .    F  H
        ~H  T
        F ~T
 
    
    a.
        Hypothetical Syllogism (HS.)
        
    
    b.
    Constructive Dilemma (CD)
        
    
    c.
    Modus Tollens (MT)
        
    
    d.
    Modus Ponens (MP)
        
    
    e.
    None of the above
5 points
Question 5
1. E  T
N E    
     (E  T) • (N E)
    
    a.
    
    
    b.
    Constructive Dilemma (CD)
        
    
    c.
    Hypothetical Syllogism (HS)
        
    
    d.
    Conjunction (Conj)
        
    
    e.
    None of the above
5 points
Question 6
1. (P Q) (~T Z)
P v ~T
Q Z
    
    a.
    Conjunction (Conj)
    
    b.
    Constructive Dilemma
    
    c.
    Simplification (Simp)
    
    d.
    Addition (Add)
    
    e.
    None of the above
5 points
Question 7
1. 6.     In the following partial proof, what is the justification for line 8 ? (This is like the 2nd exercise in book, except I am only asking you to identify 1 line instead of every line in a completed proof.)
 
1.     A (B  C)
2.     D (C A)
3.     D  A
4.     D /  B
5.     A        3, 4 DS
6.     B  C    1, 5 MP
7.     C A    2, 4 MP
                                                8.      B A    _______
    
    a.
     1, 2...
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