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Prove that the following propositions are tautologies using rules of inference. a) ((p^q) ^ (pvq)) b) -(p-->q) --> p

Prove that the following propositions are tautologies using rules of inference. a) ((p^q) ^ (pvq)) b) -(p-->q) --> p

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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Can you please help me prove that the following propositions in the first image attached are tautologies using the RULES OF INFERENCE!!! (which can be found in the second image I have attached)

Prove that the following propositions are tautologies using rules of inference. a) -((p^q) ^ ~(pvq)) b) -(p-->q) --> p
Transcribed Image Text:Prove that the following propositions are tautologies using rules of inference. a) -((p^q) ^ ~(pvq)) b) -(p-->q) --> p
itions: Logic and Proofs TABLE 1 Rules of Inference. Rule of Inference P P-9 :. 9 -q P-9 קר . P-9 9-r .. pr PV q P :.qu P :: pv q p^ q .. P P 9 :. p^g pv q pvr :: qvr Tautology (p^(p-q)) → 9 (-q ^ (p →q)) ((p →q) ^ (q→r)) → (p → r) → P - ((pvq) ^-p) → 9 P→ (pv q) (p^q) → р ((p) ^ (q)) → (p^q) ((pvq) ^ (p Vr)) → (qvr) This is an argument that uses the addition rule. Name Modus ponens Modus tollens Hypothetical syllogism Disjunctive syllogism Addition Simplification Conjunction Resolution LE 4 State which rule of inference is the basis of the following argument: "It is below raining now. Therefore, it is below freezing now." Solution: Let p be the proposition "It is below freezing now," and let q be the prop raining now." This argument is of the form si botellons de l on biley sus to estu
Transcribed Image Text:itions: Logic and Proofs TABLE 1 Rules of Inference. Rule of Inference P P-9 :. 9 -q P-9 קר . P-9 9-r .. pr PV q P :.qu P :: pv q p^ q .. P P 9 :. p^g pv q pvr :: qvr Tautology (p^(p-q)) → 9 (-q ^ (p →q)) ((p →q) ^ (q→r)) → (p → r) → P - ((pvq) ^-p) → 9 P→ (pv q) (p^q) → р ((p) ^ (q)) → (p^q) ((pvq) ^ (p Vr)) → (qvr) This is an argument that uses the addition rule. Name Modus ponens Modus tollens Hypothetical syllogism Disjunctive syllogism Addition Simplification Conjunction Resolution LE 4 State which rule of inference is the basis of the following argument: "It is below raining now. Therefore, it is below freezing now." Solution: Let p be the proposition "It is below freezing now," and let q be the prop raining now." This argument is of the form si botellons de l on biley sus to estu
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