3. Show that the premises "It is not Sunny this afternoon and it is colder than yesterday." "We will go swimming only if it is Sunny," "If we do not go swimming then we will take a Canoe trip." and "If we take canoe trip then we will be home by sunset" lead to the conclusion "We will be home by sunset."
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- With this exercise, we shall develop a solution to the following riddle. Two adults, their three children, and their dog are on a walk when they come upon a river. They have a boat, but it can only hold a maximum of one adult with either one child or the dog; or three chidren; or two children and the dog. Anyone (other than the dog) can row the boat; but it would be too much work for one child to row across by themself. How can they all get across the river? You are required to solve this riddle by modelling it using a labelled transition system (LTS). 1. What are the states of your LTS consist of? Make sure you consider all the aspects of the riddle. Justify your notion of state. 2. What are the actions of your LTS? List all the actions. Justify your choice of actions. 3. Drawing out the entire LTS may be a time consuming task as there could be very many states and transitions. However, drawing out only part of the LTS is doable. Draw part of the LTS, anywhere between 7 and 12…a)A thief robbing a store finds 5 items; the items are worth 8,10,7,20 and 11 dollars and weights 2,3,2,7 and 7 pounds. He wants to take as valuable a load as possible, but he can carry at most 9 pounds in his knapsack. What is the maximum worth of items that he can take? b) What if the thief somehow managed to increase the capacity of his knapsack by 2 pounds? What will be the maximum worth of items that he can take then?2. A man must ferry a goat, a wolf, and a head of cabbage across a river. The available boat, however, can carry only the man and one other thing. The goat cannot be left with the cabbage, nor can the wolf be left with the goat. How should the man ferry the three items across the river?
- Problem 5 (#2.1.36).Find the truth set of each of these predicates where the domain is the set of integers. a) P(x) : “x3≥1” b) Q(x) : “x2= 2” c) R(x) : “x < x2”3. A technician takes X hours to visit the stores in a couple of streets in one shift, and when he finishes his tour, another technician revisits the same stores again, needing other X hours to finish the second shift, and so on. For example, if the first technician started his shift at 1:00pm, he finishes it at 7:00pm and the second technician starts his shift at 7:00pm and finishes it at 1:00am, and so on. The supervisors used to make a quick meeting with all technicians twice a day at 1:00 am and 1:00 pm, so they need to finish their tours exactly 1:00. Identify the mathematical notation for the number of shifts should be made by the technicians in order to achieve this, write the name of this mathematical value, and find it for two tours, one with X=7 and another with X = 11 .John is training for a marathon and he can easily alternate between running a mile and walking a mile. If he runs for 2 miles in a row, he becomes fatigued, and must then walk for 2 miles in a row in order to no longer be fatigued. When he is fatigued, he can still alternate between running a mile and walking a mile, but if he runs 2 miles in a row while already fatigued, he will collapse on the side of the road. If he runs 3 miles in a row at any point, he will also collapse. Let the letter 'a' stand for John running 1 mile, and the letter 'b' stand for John walking 1 mile. Draw a DFA which accepts all possible runs in which John does not collapse on the side of the road.
- 2. A certain company gives commission to each of their salesmen based from the type of appliance sold andthe price of the appliance. Below are the given rates that will be used in computing for the salesman’scommission:If type is Commission is2, 5, 6 15% of the price4, 8, 10 20% of the price3, 1, 9,7 25% of the priceInput salesman’s name, type of appliance sold, and price of the appliance. Compute and print thesalesman’s commission.2. A safe has 5 locks v, w, y and z; all of which must be unlocked for the safe to open. The keys to the locks are distributed among five executives in the following manner.Mr. A has keys for locks v and x. Mr. B has keys for locks v and y. Mr. C has keys for locks w and y. Mr. D has keys for locks x and z. Mr. E has keys for locks v and z.a) Determine the minimal number of executives required to open the safe.b) Find all the combinations of executives that can open the safe; write and expression f(A, B, C, D, E) which specifies when the safe can be opened as a function of what executives are present.c) Who is the essential executive?Each year a certain amount of money is deposited in an account which pays an annual interest rate of are so that at the end of the year the balance in the account is multiplied by a growth factor of X equals 2+ R. $500 is deposited at the start of the first year, an additional 200 is deposited at the start of the second year, and 600 and start of the following year
- Represent each of the following sentences by a Boolean equation. C. The company safe should be unlocked only when Mr. Jones is in the office or Mr. Evans is in the office,Given each pair of propositions ? and ? determine in each case whether or not ? ≡ ?.? = ? ∧ (¬ ? ∨ ?),? = ? ∨ (? ∧ ¬ ?) and ? = (? → ?) → ?,? = ? → (? → ?)1. Let ?, ?, ? be the propositions? ∶ Grizzly bears have not been seen in the area.?: Hiking is safe on the trail.?: Berries are ripe along the trail.Write these propositions using ?, ?, ? and logical connectives.a) Berries are ripe along the trail, but grizzly bears have not been seen in the area.b) For hiking on the trail to be safe, it is necessary but not sufficient that berries not be ripe along the trail and for grizzly bears not to have been seen in the area.