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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. 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

Advanced Engineering Mathematics
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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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
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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