discrete math Question B1:Several common rules of inference are given below.P→qP..qP→qqP(Modus Ponens)(Modus Tollens)P→qq→r..prpv qP..q(Hypothetical Syllogism)(Disjunctive Syllogism)P..pv qP9..p^q(Addition)(Conjunction)(a) Use rules of inference to construct a valid argument that uses the premises p, pq, r →q to reachthe conclusion r. In each step, state explicitly what rule of inference you are using.(b) You are given the following three premises:(i) There is a lifeguard shortage.(ii) If there is a lifeguard shortage, then the pools are closed.(iii) If the waterslide is running, then the pools are open.Do you have enough information to logically conclude whether or not it the waterslide is running?Explain how to reach a conclusion, or describe what extra information you require.Hint: assign appropriate propositional variables, and use the conclusion of part (a).

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Answered: (a) Use rules of inference to construct…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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