(PVQ)→ R RVS 2. P-

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 10CT: Statement P and Q are true while R is a false statement. Classify as true or false:...
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Question

Complete the following indirect proof by contradiction.

 

See the example for basis.

(PvQ)→ くR
RVS
P- ~Q
2.
:P S
Proof
Statement
1.(PVQ)→ ~R
RVS
Justification
Premise
1.
Premise
2.
Presmise
~(P-→S)
Preliminary Assumphon.
4.
3.
La
Transcribed Image Text:(PvQ)→ くR RVS P- ~Q 2. :P S Proof Statement 1.(PVQ)→ ~R RVS Justification Premise 1. Premise 2. Presmise ~(P-→S) Preliminary Assumphon. 4. 3. La
(¬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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