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Answered Same Day Oct 14, 2021

Solution

Yasodharan answered on Oct 15 2021

133 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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Bottom of Form
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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