(a) Use rules of inference to construct a valid argument that uses the premises p, p→¬q, r→q to reach the 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).
(a) Use rules of inference to construct a valid argument that uses the premises p, p→¬q, r→q to reach the 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).
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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discrete math
Transcribed Image Text:Question B1:
Several common rules of inference are given below.
P→q
P
..q
P→q
q
P
(Modus Ponens)
(Modus Tollens)
P→q
q→r
..pr
pv q
P
..q
(Hypothetical Syllogism)
(Disjunctive Syllogism)
P
..pv q
P
9
..p^q
(Addition)
(Conjunction)
(a) Use rules of inference to construct a valid argument that uses the premises p, pq, r →q to reach
the 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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