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# for sam

## Solution

Yasodharan answered on Oct 15 2021
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.

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.

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.

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...
SOLUTION.PDF