2. Give a reason to justify each step of the proof. Use the following Rules of Inference for Propositional Logic, Converse, Contrapositive, and Inverse. 1. SAU 2. u Steps Reason 1. s^u Modus Modus Disjunctive Modus Hypothetical Ponens Simplification Ponens Syllogism Premise from 4 and Tolle Resolution from 1 from 9 and Conjunction Modus from 2 from 1 from 12 from 8 from 6 and 7 5 and 3 and 13 and 9 and 4 14 O 2 u O Conclusion: 0 0 00 O ο ο
2. Give a reason to justify each step of the proof. Use the following Rules of Inference for Propositional Logic, Converse, Contrapositive, and Inverse. 1. SAU 2. u Steps Reason 1. s^u Modus Modus Disjunctive Modus Hypothetical Ponens Simplification Ponens Syllogism Premise from 4 and Tolle Resolution from 1 from 9 and Conjunction Modus from 2 from 1 from 12 from 8 from 6 and 7 5 and 3 and 13 and 9 and 4 14 O 2 u O Conclusion: 0 0 00 O ο ο
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 7RE
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![2. Give a reason to justify each step of the proof. Use the following Rules of
Inference for Propositional Logic, Converse, Contrapositive, and Inverse.
1. s Au
2. u
3. u → t
4. t
5. s
6. s At
7. (s^t) ->T
8.-r
9. (pvq)
10.pv q
11. p V t
12.qvt
13.-q
14.t
Steps
Premises :
SAU
u t
(s^t) → -r
(pvq) → r
-pvt
-q
Reason
1. s^u
2. u
3. u →
t
4. t
5.s
6.s^t
7. (s^
t) → -r
8. -r
9. (p v
q) → r
10. p v
q
11. p
vt
12. qv
t
13. -q
14. t
Conclusion:
t
Modus
Modus Disjunctive
Ponens Simplification Ponens Syllogism
from 2 from 1 from 6 from 12
and 3
and 7 and 13
O
Conjunction
Premise from 4 and
5
Modus
Tollens
from 8
and 9
Resolution
Modus Hypothetical
Ponens Syllogism
from 1 from 9 and
and 4
14](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8fd0fb9a-6ec0-4ab2-bd51-954f524ff43d%2Fe7b9c04d-62e0-4845-ac93-3ca25d9df5b3%2F1blpxpr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Give a reason to justify each step of the proof. Use the following Rules of
Inference for Propositional Logic, Converse, Contrapositive, and Inverse.
1. s Au
2. u
3. u → t
4. t
5. s
6. s At
7. (s^t) ->T
8.-r
9. (pvq)
10.pv q
11. p V t
12.qvt
13.-q
14.t
Steps
Premises :
SAU
u t
(s^t) → -r
(pvq) → r
-pvt
-q
Reason
1. s^u
2. u
3. u →
t
4. t
5.s
6.s^t
7. (s^
t) → -r
8. -r
9. (p v
q) → r
10. p v
q
11. p
vt
12. qv
t
13. -q
14. t
Conclusion:
t
Modus
Modus Disjunctive
Ponens Simplification Ponens Syllogism
from 2 from 1 from 6 from 12
and 3
and 7 and 13
O
Conjunction
Premise from 4 and
5
Modus
Tollens
from 8
and 9
Resolution
Modus Hypothetical
Ponens Syllogism
from 1 from 9 and
and 4
14
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