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- PROBLEM 10. [TIME ALLOWED = 5 MINUTES] Express the following propositions using logical connectives: (a) I will go to the movie if I complete my assignment. (b) I will go to the movie only if I complete my assignment. (c) I will not go to the movie if I do not complete my assignment.1- If the rat ate the cheese or the rat is not in the trap, then it is under the bed. The Rat is neither under the bed nor under the table. You will see the Rat Footprint unless It is under the table, or it is not in the trap. The Rat drinks the water if you see its footprint. The rat ate the cheese, or it did not eat the newspaper. Therefore, if the rat neither under the table nor under the bed, then it did not eat the newspaper but it drank the water. a. Covert the above argument into symbolic. b. Show that the argument is valid.PROBLEM 14. [TIME ALLOWED = 5 MINUTES] Let p and q be the propositions: p : I bought a lottery ticket this week. q : I won the million dollar jackpot on Friday. The proposition (p q) as an English sentence is: (a) I did not buy a lottery ticket this week, and I did not win the million dollar jackpot on Friday. (b) Either I bought a lottery ticket this week or I won the million dollar jackpot on Friday. (c) Not better than good beer. (d) None of the above.
- 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 .Express each of the following statements using predicates and quantifiers. A student must take at least 60 course hours, or at least 45 course hours and write a master’s thesis, and receive a grade no lower than a B in all required courses, to receive a master’s degree. A man qualifies for the marathon if his best previous time is less than 3 hours and a woman qualifies for the marathon if her best previous time is less than 3.5 hours.3. Consider the rules Age > 40 ⇒ Donor and Age ≤ 50 ⇒￢Donor. a. Are these two rules mutually exclusive? b. Are these two rules exhaustive?
- PROBLEM 2. [TIME ALLOWED = 5 MINUTES] Is the following sentence a proposition? If it is a proposition, determine whether it is true or false.The statement "Every yellow dog has fleas" together with the statement "Fido is a blue dog". Which of the following is TRUE about the given premises. a.)modus tollens b.)modus ponens c.)modus ponens does not apply d.)modus tollens does not applyThree persons P1, P2, and P3 were invited by their friend F to make some smørbrød (sandwich made of bread, eggs, and tomato) together. To make a portion of smørbrød, three ingredients are needed: a slice of bread, a slice of tomato, and a slice of an egg. Each of these persons P1, P2, P3 has only one type of each of the ingredients: person P1 has slices of bread person P2 has slices of tomato; person P3 has slices of egg. We assume that persons P1, P2, and P3 each has an unlimited supply of these ingredients (i.e., slices of bread, slices of tomato, slices of egg), respectively. Their friend F, who invited them, also has an unlimited supply of all the ingredients. Here is what happens: the host F puts two random ingredients on the table. Then the invited person who has the third ingredient picks up these other two ingredients, and makes the smørbrød (i.e., takes a slice of bread, puts on it a slice of tomato, and puts on top a slice of egg), and then eats the smørbrød. The host of…
- Problem 5: Determine which rule of inference is used in each of the following arguments. 1. Alice is a Mathematics major. Therefore, Alice is either a Mathematics major or a computer science major.2. Jerry is a Mathematics major and a computer science major. Therefore, Jerry is a Mathematics major.3. If it is rainy, then the pool will be closed. It is rainy. Therefore, the pool is closed.4. If it snows today, the university will close. The university is not closed today. Therefore,it did not snow today.5. If I go swimming, then I will stay in the sun too long. If I stay in the sun too long, then I will sunburn. Therefore, if I go swimming, then I will sunburn.6. If Socrates is human, then Socrates is mortal. Socrates is human. Thus, Socrates is mortal.Problem 5. An Electricity board charges the following rates mentioned in the table for the use of electricity. All users are charged Taka 50 as a meter charge for every month. If any user wants to change/replace his meter, he will be charged taka 2000. The monthly bill will be generated based on ● Customer Category ● Consumed Units ● Phase ● For Category 3 and 5 along with other parameters, you need to also consider flat rate, peak time, and off-peak time. Take input from the user, how many units were consumed during flat rate, peak, or off-peak time. ● Meter Charge Write a program to read the name of the user, Customer Category, Phase, number of units consumed and print out the monthly bill. Note that ● Phase, flat rate, peak time and off-peak time will be appeared based on the customer category. ● The monthly bill will be calculated following the number of Days in a month2. 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?
