Consider proving the following argument: You are given the first three steps of the proofs: 1. Hypothesis: pq 2. Hypothesis: pr 3. Simplification, 2: p B. Hypothesis C. Conditional identity, 5 D. Modus ponens, 6, 8 E. Additio 5 F. Conjunction. 4. 9 G. Conditional identity, 5 P→q Vu Your task is to complete the proof using as few lines as possible and using only the following inferences: A. Modus tollens, 1, 3 H. Simplification, 7 L. Conjunction. 4. 6 J. Modus ponens, 1, 3 K. Modus ponens, 6, 8 PAr qAu L. De Morgan's law, 5 M. Commutative law, 2 N. Simplification, 5 Write your answer for steps 4 onward as a string, consisting of the rules you have applied in order, e.g.. BDFAC. Note that while there may be other ways to prove the argument, you are required to use only the lines A-N given above. In addition, your proof should not include any redundant step, that is, no step that is not necessary for your proof.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 6CT: Name the type of reasoning used in the following scenario. While shopping for a new television,...
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Consider proving the following argument:
p→q
Vu
You are given the first three steps of the proofs:
1. Hypothesis: pq
2. Hypothesis: pr
3. Simplification, 2: p
B. Hypothesis
C. Conditional identity, 5
D. Modus ponens, 6, 8
E. Additio 5
Your task is to complete the proof using as few lines as possible and using only the following inferences:
A. Modus tollens, 1, 3
F. Conjunction. 4, 9
G. Conditional identity. 5
PAr
H. Simplification, 7
I. Conjunction, 4,6
J. Modus ponens, 1, 3
K. Modus ponens, 6, 8
qAu
L. De Morgan's law, 5
M. Commutative law, 2
N. Simplification, 5
Write your answer for steps 4 onward as a string, consisting of the rules you have applied in order, e.g..
BDFAC. Note that while there may be other ways to prove the argument, you are required to use only the
lines A-N given above. In addition, your proof should not include any redundant step, that is, no step that
is not necessary for your proof.
Transcribed Image Text:@ Consider proving the following argument: p→q Vu You are given the first three steps of the proofs: 1. Hypothesis: pq 2. Hypothesis: pr 3. Simplification, 2: p B. Hypothesis C. Conditional identity, 5 D. Modus ponens, 6, 8 E. Additio 5 Your task is to complete the proof using as few lines as possible and using only the following inferences: A. Modus tollens, 1, 3 F. Conjunction. 4, 9 G. Conditional identity. 5 PAr H. Simplification, 7 I. Conjunction, 4,6 J. Modus ponens, 1, 3 K. Modus ponens, 6, 8 qAu L. De Morgan's law, 5 M. Commutative law, 2 N. Simplification, 5 Write your answer for steps 4 onward as a string, consisting of the rules you have applied in order, e.g.. BDFAC. Note that while there may be other ways to prove the argument, you are required to use only the lines A-N given above. In addition, your proof should not include any redundant step, that is, no step that is not necessary for your proof.
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