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Subject
Philosophy
Date
Apr 3, 2024
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11
Uploaded by MagistrateLightning8384
9/25/22, 11
:
54 PM
L04 - Practice Quiz: [22FA] PHIL 12, Sec 1: Symbolic Logic (Fisher)
Page 1 of 11
https://psu.instructure.com/courses/2204563/quizzes/4533204
L04 - Practice Quiz
Due
Sep 25 at 11:59pm
Points
10
Questions
10
Time Limit
60 Minutes
Allowed Attempts
3
Instructions
Attempt History
Attempt
Time
Score
LATEST
Attempt 1 9 minutes
4.33 out of 10
Score for this attempt: 4.33
out of 10
Submitted Sep 25 at 11:53pm
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Take the Quiz Again
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L04 - Practice Quiz: [22FA] PHIL 12, Sec 1: Symbolic Logic (Fisher)
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This attempt took 9 minutes.
1 / 1 pts
Question 1
Suppose we were to test the following argument to determine whether
or not it is deductively valid (a case of semantic entailment): . The first step of using the truth-tree
test is to setup the tree into what is called the stack''. Which one of the
following formulas would NOT
be in the initial stack:
Correct!
Correct!
0 / 1 pts
Question 2
Suppose we were to test the following argument to determine whether
or not it is deductively valid (a case of semantic entailment): . The first step of using the truth-
tree test is to setup the tree into what is called the stack''. Which one of
the following formulas would NOT
be in the initial stack:
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L04 - Practice Quiz: [22FA] PHIL 12, Sec 1: Symbolic Logic (Fisher)
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orrect Answer
orrect Answer
ou Answered
ou Answered
When using the truth-tree method to test an argument for
deductive validity, the tree is formed by stacking the premises
and the literal negation of the conclusion. The non-negated
version of the conclusion should NOT appear in the stack. The
literal negation of the conclusion ¬ M is ¬ ¬ M . This means that
¬ ¬ M should appear in the stack. Since each of the other
options here is one of the premises of the argument, each of
them should be in the stack as well. A truth tree is a means of
checking whether there is some way of assigning a truth value to
each of the atomic propositions that occurs in the stack (in this
case, P , R , S , T , and M ) such that all of the propositions in
the stack turn out to be true. By including the negation of the
conclusion, we are using the truth tree to test whether it is
possible to assign these values in such a way that the premises
and the negation of the conclusion are true. In other words, we
are using it to test whether it is possible for the premises to be
true and the conclusion false. For more on how to set up the
truth tree, see PL Truth Trees - Part 1
(https://youtu.be/YdTTdArmUKA) . For more on how to use the
truth-tree method to determine if a PL argument is deductively
valid, see PL Truth Trees - Validity
(https://youtu.be/l3bqzTixAls) and see Agler Symbolic Logic
(1st
ed.), pp.148-150. For more on literal negation, see PL Syntax
Part 3 (Literal negation)
(https://youtu.be/8QUaFqIkwDQ?
t=2m4s) and Agler Symbolic Logic (1st ed.), pp.42-43.
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L04 - Practice Quiz: [22FA] PHIL 12, Sec 1: Symbolic Logic (Fisher)
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0 / 1 pts
Question 3
What decomposition rule should you use on the following wff:
ou Answered
ou Answered
orrect Answer
orrect Answer
0 / 1 pts
Question 4
What decomposition rule should you use on the following wff: ou Answered
ou Answered
orrect Answer
orrect Answer
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L04 - Practice Quiz: [22FA] PHIL 12, Sec 1: Symbolic Logic (Fisher)
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0.67 / 1 pts
Question 5
Answer 1:
Answer 2:
Answer 3:
(To answer the following question, type upper case T or F): Assign an
interpretation to T
, F
, and F
assuming the
following literal wffs were recovered from a completed open branch of a
truth tree: T
Correct!
Correct!
F
ou Answered
ou Answered
T orrect Answer
orrect Answer
F
Correct!
Correct!
0.67 / 1 pts
Question 6
(To answer the following question, type upper case T or F): Assign an
interpretation to T
, T
, and F
assuming the
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L04 - Practice Quiz: [22FA] PHIL 12, Sec 1: Symbolic Logic (Fisher)
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Answer 1:
Answer 2:
Answer 3:
following literal wffs were recovered from a completed open branch of a
truth tree: T
Correct!
Correct!
T
ou Answered
ou Answered
F orrect Answer
orrect Answer
F
Correct!
Correct!
0 / 1 pts
Question 7
The following argument is invalid: . Which
assignment of truth values to the propositional letters (or their literal
negations) shows the argument to be invalid? Use the truth-tree
procedure (using either Proof Tools
or pen/pencil and paper) to help
you determine the answer. In other words, use the truth-tree method to
pick out a valuation that shows that the argument is deductively invalid.
.
.
ou Answered
ou Answered
.
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L04 - Practice Quiz: [22FA] PHIL 12, Sec 1: Symbolic Logic (Fisher)
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.
orrect Answer
orrect Answer
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The truth-tree method reveals that there is at least one open
branch. This branch contains . Thus, the valuation
where provides the
counter-example that shows us that the argument is invalid.
Reasoning without the truth tree, we can see this is the case as
well. The conclusion of the argument is . Thus, in order to
show that the argument is invalid, it must be the case that
or . Also, in order to show the above
argument to be invalid, the premises must be true. Since one of
the premises is , it must be the case that . If
and , then the . This
means that the consequent of our first premise is
false. In order for the premise itself to be true, then, the
antecedent has to be false as well. Thus, when the
, all of the premises turn
out to be true and the conclusion turns out to be false. Thus, the
valuation where provides
our counter-example. For more on how to use a truth tree to
determine a valuation (truth-value assignment), see Agler
Symbolic Logic
((1st ed.), Sec. 4.6.1 (pp.138-141). For the
definition of a "valuation", see Agler Symbolic Logic
((1st ed.), pp.
65-68, 96, 139-141. For how to use a truth tree to test an
argument for validity and invalidity, see Agler Symbolic Logic
(1st
ed.), Sec. 4.6.5 (pp.148-150). Note:
while you may have solved
this problem using a truth table rather than a truth tree, it is
important that you learn the truth-tree method as the truth-table
method will not work for a more expressive kind of logic
considered later. For the difference between trees and tables,
see Agler Symbolic Logic
(1st ed.), p.99; see also Lesson 4:
Trees vs. Tables
.
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L04 - Practice Quiz: [22FA] PHIL 12, Sec 1: Symbolic Logic (Fisher)
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0 / 1 pts
Question 8
Use the truth-tree decision procedure (relying on Proof Tools
or
pen/pencil and paper) to determine whether is deductively
valid.
consistent. invalid. orrect Answer
orrect Answer
valid. ou Answered
ou Answered
undecideable. A truth tree test for the argument shows this
argument to be invalid. Decomposing the stack that consists of
the premises and the negation of the conclusion yields a tree
that has one completed open branch. The branch where v ( P ) =
T and v ( ¬ Q ) = T shows us that it is possible for all the
premises to be true while the conclusion is false. P ∨
Q ⊢
Q is
often confused with the valid argument P ∧
Q ⊢
Q . Remember
that P ∨
Q can be translated as " P or Q ". As a disjunction " P or
Q " is true if either P is true or Q is true. This means it is logically
possible for a disjunction " P or Q " to be true when " Q " turns
out to be false. More concretely, imagine the following argument:
"John will either go to the store or watch a movie. Therefore,
John will watch a movie." This argument is invalid as it is
possible that "John will either go to the store or watch a movie"
is true but "John will watch a movie" is false, e.g. when John
decides not to watch a movie but to go to the store instead.
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L04 - Practice Quiz: [22FA] PHIL 12, Sec 1: Symbolic Logic (Fisher)
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1 / 1 pts
Question 9
Under what condition does the truth-tree test show a set (collection) of
propositions to be consistent?
under the condition that determines a closed tree.
under the condition that determines a completed
open tree.
under the condition that determines a closed tree.
under the condition that determines a completed open
tree.
Correct!
Correct!
1 / 1 pts
Question 10
When is a branch in a truth tree fully decomposed?
A branch is fully decomposed when most of the propositions in the
branch that can be decomposed have been decomposed.
A branch is fully decomposed when the tree is closed.
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L04 - Practice Quiz: [22FA] PHIL 12, Sec 1: Symbolic Logic (Fisher)
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A branch is fully decomposed when there is at least one branch that is
completed decomposed.
A branch is fully decomposed when all propositions in the branch that
can be decomposed have been decomposed.
Correct!
Correct!
For a definition of a fully decomposed branch", see Agler (1st
ed.), pp. 110-111.
Quiz Score: 4.33
out of 10