TABLE 1.14 More Inference Rules From Can Derive Name/Abbreviation for Rule P→Q, Q→R PVQ, P' P→R[Example 16] Hypothetical syllogism-hs Q [Exercise 25] Q' →P' [Exercise 26] Disjunctive syllogism–ds Contraposition-cont Q' → P' P→Q [Exercise 27] Contraposition-cont PAP[Exercise 28] Self-reference-self PVP P[Exercise 29] Self-reference-self (РЛО) —R P→(Q→R) [Exercise 30] Exportation-exp Q [Exercise 31] (PAQ) V (PAR) [Exercise 32] (PVQ) A (P V R) [Exercise 33] P, P' Inconsistency-Inc PA (QVR) Distributive-dist PV (QAR) Distributive-dist

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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write the argument using propositional wffs (use the statement letters shown). Then, using propositional logic,

Russia was a superior power, and either France was not strong or Napoleon made an error. Napoleon did not make an error, but if the army did not fail, then France was strong. Hence, the army failed and Russia was a superior power. R, F, N, A

TABLE 1.14
More Inference Rules
From
Can Derive
Name/Abbreviation for Rule
P→Q, Q→R
PVQ, P'
P→R[Example 16]
Hypothetical syllogism-hs
Q [Exercise 25]
Q' →P' [Exercise 26]
Disjunctive syllogism–ds
Contraposition-cont
Q' → P'
P→Q [Exercise 27]
Contraposition-cont
PAP[Exercise 28]
Self-reference-self
PVP
P[Exercise 29]
Self-reference-self
(РЛО) —R
P→(Q→R) [Exercise 30]
Exportation-exp
Q [Exercise 31]
(PAQ) V (PAR) [Exercise 32]
(PVQ) A (P V R) [Exercise 33]
P, P'
Inconsistency-Inc
PA (QVR)
Distributive-dist
PV (QAR)
Distributive-dist
Transcribed Image Text:TABLE 1.14 More Inference Rules From Can Derive Name/Abbreviation for Rule P→Q, Q→R PVQ, P' P→R[Example 16] Hypothetical syllogism-hs Q [Exercise 25] Q' →P' [Exercise 26] Disjunctive syllogism–ds Contraposition-cont Q' → P' P→Q [Exercise 27] Contraposition-cont PAP[Exercise 28] Self-reference-self PVP P[Exercise 29] Self-reference-self (РЛО) —R P→(Q→R) [Exercise 30] Exportation-exp Q [Exercise 31] (PAQ) V (PAR) [Exercise 32] (PVQ) A (P V R) [Exercise 33] P, P' Inconsistency-Inc PA (QVR) Distributive-dist PV (QAR) Distributive-dist
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