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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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q2 (c ) Plz do according to question requirements PLz i need it hundred percent exact answer plz
@
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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