Which of the following indicates a difference between the converse and contraposition of a conditional proposition?
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- Consider the following true propositions:• p : The applicant has passed the learner permit test.• q : The applicant has passed the road test.• r : The applicant is allowed a driver’s license.For each of the following sentences write,symbolically, the compound proposition that correspondstothe given sentence in English asit is written (do not change the order or form of the expression).a) The applicant did not pass the road test but passed the learner permit test.b) If the applicant passes the learner permit test and the road test, then the applicant is allowed adriver’s license.c) Passing the learner permit test and the road test are necessary for being allowed a driver’slicense.d) The applicant passed either the learner permit test or the road test, but not both.e) It is not true that the applicant does not pass the road test and is allowed a driver’s license.Question 5The dual of the following logical expression x'y+xy' isDefine the following propositions:• s: a person is a senior• y: a person is at least 17 years of age• p: a person is allowed to park in the school parking lotExpress each of the following English sentences with a logical expression:b) A person can park in the school parking lot if they are a senior or at least seventeen yearsof age.s v y --> p (answer) I am confused here. Would p --> s v y mean the same?
- Translate the following statements into logical expressions using predicates, quantifiers, and logical connectives. Predicates: C(x):xis a CSC510 student .L(x):xloves programming. Universe of discourse for the variablexis all students. i) Every student loves programming. ii) Every CSC 510 student loves programming .iii) Some CSC 510 students love programming.Construct a conditional proof of validity for the given argument below using the rules of inference and equivalence 1. (A ∧ B) → (∼ C → D) B∧ ∼ C ∴ A → D (use conditional proof of validity)QUESTION 3 Consider the following propositions : p: "I finish my Work" q: "I play handball" r: "The sun is shining" s: "The humidity is low" The symbolic of the following sentence "I finish my work and I play handball unless the humidity is not low and the sun is not shining" is : not s logical and not r rightwards arrow not p logical or not q None of all the proposed answers s logical or r rightwards arrow p logical and q s logical and r rightwards arrow p logical or q not p logical or not q rightwards arrow not s logical and not r
- Which of the following are admissible, given admissible heuristics h1, h2? Which of the following are consistent, given consistent heuristics h1, h2? Justify your answer.Exercise 1.1.1: Identifying propositions. infoAbout Determine whether each of the following sentences is a proposition. If the sentence is a proposition, then write its negation. (a) Have a nice day. (b) The soup is cold. (c) The patient has diabetes. (d) The light is on. (e) It's a beautiful day. (f) Do you like my new shoes? (g) The sky is purple. (h) 2 + 3 = 6 (i) Every prime number is even. (j) There is a number that is larger than 17.Exercise 7-4 Symbolize the following sentences, letting Px = “x was U.S. president”; Ix = “x is (was) well informed”; d = “Donald Trump”; and b = “George W. Bush.” 1. All U.S. presidents have been well informed. 3. Not all U.S. presidents have been well informed. 5. But not all U.S. presidents have been ill-informed (not well informed) if George W. Bush was well informed. Now let Sx = “x is a logic student”; Lx = “x is logical”; Px = “x is popular”; and a = “Art.” 7. Logic students are logical. 9. Well, not all logic students are logical. 11.So if all logic students are logical, none of them is popular. 13. Nor is it true that those who are unpopular all are illogical. 15.
- Computer Science Consider each of the following four sentences and say whether they would typically be used to make a statement or not to make a statement: Where is it? There it is! Watch out! It's coming toward us too fast! If the if-part of a conditional claim is true, and if the conditional claim itself is true, will the then-part have to be true? (draw and use the truth table for the conditional in your answer)Exercise 1.3.3: Truth values for the inverse, contrapositive, and converse of a conditional statement. infoAbout State the inverse, contrapositive, and converse of each conditional statement. Then indicate whether the inverse, contrapositive, and converse are true. (a) If 3 is a prime number then 5 is an even number. (b) If 7 < 5, then 5 < 3. (c) If 5 is a negative number, then 3 is a positive number.Consider the following propositions: p="It is cloudy" q="It is rainy" r="I will play outside" s="I will stay at home" Select the symbolic (s) of the the following sentence: "I will not stay at home and and I will play outside when it is cloudy and not rainy"