(PVQ)→R RVS 2. Proof Statement (PVQ)>~R RVS Justification Premise Premise 2. Presmise

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question

Complete the following indirect proof by contradiction. Also, show how every step happen.

 

See the example for basis.

(PVQ)→R
RVS
Proof
Statement
1(PVQ)> ~R
RVS
P→~Q
~(P-→S)
Justification
Premise
Premise
2.
Presmise
13
Preliminany Assumphon
4.
Transcribed Image Text:(PVQ)→R RVS Proof Statement 1(PVQ)> ~R RVS P→~Q ~(P-→S) Justification Premise Premise 2. Presmise 13 Preliminany Assumphon 4.
(¬B V C) → A Premise
Premise
1.
2.
B → D
3.
Cv -D
Premise
Premise - proof by contradiction
Modus tollens (1, 4)
DeMorgan (5)
Decomposing a conjunction (6)
Decomposing a conjunction (6)
Modus ponens (2, 7)
Disjunctive syllogism (3, 9)
Constructing a conjunction (8, 10)
Proof by contradiction (4, 11)
4.
-A
-(-B v C)
BA-C
5.
6.
7.
В
8.
-C
9.
D
10. С
11. Сл-С
12. А
Transcribed Image Text:(¬B V C) → A Premise Premise 1. 2. B → D 3. Cv -D Premise Premise - proof by contradiction Modus tollens (1, 4) DeMorgan (5) Decomposing a conjunction (6) Decomposing a conjunction (6) Modus ponens (2, 7) Disjunctive syllogism (3, 9) Constructing a conjunction (8, 10) Proof by contradiction (4, 11) 4. -A -(-B v C) BA-C 5. 6. 7. В 8. -C 9. D 10. С 11. Сл-С 12. А
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