hat is the corresponding: Gardener(John)^[¬Like(john, m)V¬Like(John, Pizza)] * O John is a Gardener who likes Pizza and Sun O John is a Gardener who likes Pizza and does not like sun O John is a Gardener who does not like Sun and Pizza John is a Gardener whn likes sun or nizza
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- Consider the following predicates defined on N + .E(n) denotes “n is even”, and P (n) denotes “n is prime”. (a) Translate the following into ordinary English.i. ∃n (P (n) ∧ E(n)).ii. ∀n (E(n) ∨ ¬P (n)).iii. ¬∀n (E(n) ∨ P (n)).code in scala def unfold[A, S](z: S)(f: S => Option[(A, S)]): LazyList[A] = f(z) match { case Some((h, s)) => h #:: unfold(s)(f) case None => LazyList() } [Note: #:: is the Cons constructor of LazyLists] A triple (x, y, z) of positive integers is pythagorean if x2 + y2 = z2. Using the functions studied in class, define a function pyth which returns the list of all pythagorean triples whose components are at most a given limit. For example, function call pyth(10) should return [(3, 4, 5), (4, 3, 5), (6, 8, 10), (8, 6, 10)]. [Hint: One way to do this is to construct a list of all triples (use unfold to create a list of integers, and then a for-comprehension to create a list of all triples), and then select the pythagorean ones.Given the following function, what happens if a[] contains just one element that doesn't match val? int binarySearch(int a[], int first, int last, int val){ if (first > last) return -1; int middle = (first + last) / 2; if (a[middle] == val) return middle; if (a[middle] < val) return binarySearch(a, middle+1, last, val); else return binarySearch(a, first, middle-1, val);} Group of answer choices binarySearch never calls itself again and terminates (recursion never happens) binarySearch calls itself once then terminates (recursion happens once) binarySearch calls itself twice then terminates (recursion happens twice) binarySearch calls itself 3 times then terminates (recursion happens 3 times)
- Please help me Josephus Problem is a theoretical problem related to a certain counting-out game. On thiscase, people are standing in a circle waiting to be executed. After a specified number ofpeople are skipped, the next person is executed. The procedure is repeated with theremaining people, starting with the next person, going in the same direction and skippingthe same number of people, until one person remains, and is freed.Arrange the numbers 1 , 2, 3 , ... consecutively (say, clockwise) in a circle. Now removenumber 2 and proceed clockwise by removing every other number, among those thatremain, until one number is left. (a) Let denote the final number which remains. Find formula for .(b) If there are 70 people, what is the safe number (the number that remains)?Implement the following Racket functions: Reflexive? Input: a list of pairs, L and a list S. Interpreting L as a binary relation over the set S, Reflexive? returns #t if L is a reflexive relation over the set S and #f otherwise. Examples: (display "Reflexive?\n") (Reflexive? '((a a) (b b) (c c)) '(a b c)) ---> #t (Reflexive? '((a a) (b b)) '(a b c)) ---> #f (Reflexive? '((a a) (a s) (b b) (c c)) '(a b c)) ---> #f (Reflexive? '() '()) ---> #t You must use recursion, and not iteration. You may not use side-effects (e.g. set!).Write a classifier algorithm for p(Y |X,α)
- A general state space search algorithm is implemented in search.py. Go through this and try to understand it. An example of how to implement a particular search problem using the state space code is shown in pitcher.py. Note in particular how the PitcherState class works in conjunction with the Search class. Using the PitcherState class as a model, write a Simpsons class that implements a solution to the following slightly modified problem from an episode of the Simpsons called Gone Maggie Gone from 2009. Homer Simpson has to move his daughter Maggie, his dog Santa's Little Helper, and a jar of medical marijuana that looks like candy across a river. He can only take one item in his boat at a time. He can't leave Maggie alone with the medical marijuana (or she will eat it) and he can't leave Santa's Little Helper alone with Maggie (because the dog will pester the girl). Formulate the actions for this problem and implement them. Be careful to ensure that illegal states are flagged…Please help. How to solve this on Java language by using only Dynamic Programming? Thank you. We are given a set A of integers. Check whether we can partition A into three subsets with equal sums. It is important to note that all elements should be included in the equally divided subsets; no element should be left out, and none of the elements should be repeated in the subsets.For example: A={4,7,6,2,10,7,10,2} has such a partition: {4,2,10}, {7,7,2},{6,10}Input: A set, A, of integersOutput: if we can partition A into three subsets with equal sums, print subsets otherwise present a suitable message.Count consecutive summers def count_consecutive_summers(n): Like a majestic wild horse waiting for the rugged hero to tame it, positive integers can be broken down as sums of consecutive positive integers in various ways. For example, the integer 42 often used as placeholder in this kind of discussions can be broken down into such a sum in four different ways: (a) 3 + 4 + 5 + 6 + 7 + 8 + 9, (b) 9 + 10 + 11 + 12, (c) 13 + 14 + 15 and (d) 42. As the last solution (d) shows, any positive integer can always be trivially expressed as a singleton sum that consists of that integer alone. Given a positive integer n, determine how many different ways it can be expressed as a sum of consecutive positive integers, and return that count. The number of ways that a positive integer n can be represented as a sum of consecutive integers is called its politeness, and can also be computed by tallying up the number of odd divisors of that number. However, note that the linked Wikipedia de0inition…
- Count consecutive summers def count_consecutive_summers(n): Like a majestic wild horse waiting for someone to come and tame it, positive integers can be broken down as sums of consecutive positive integers in various ways. For example, the integer 42 often used as placeholder in this kind of discussions can be broken down into such a sum in four different ways: (a) 3 + 4 + 5 + 6 + 7 + 8 + 9, (b) 9 + 10 + 11 + 12, (c) 13 + 14 + 15 and (d) 42. As the last solution (d) shows, any positive integer can always be trivially expressed as a singleton sum that consists of that integer alone. Given a positive integer n, determine how many different ways it can be expressed as a sum of consecutive positive integers, and return that count. The count of how many different ways a positive integer n can be represented as a sum of consecutive integers is also called its politeness, and can be alternatively computed by counting how many odd divisors that number has. However, note that the linked…Suppose P(x,y) is some binary predicate defined on a very narrow domain ofdiscourse: just the integers 1, 2, 3, and 4. Based on the following table, P(x,y) is trueor false for each of the 16 pairs of these numbers (x values are rows, y values arecolumns).1 2 3 41 T F F F2 F T T F3 T T T T4 F F F FFor example, P(1, 3) is false, as indicated by the F in the first row, third column.Use the table to decide whether the following statements are true or false.a. ∀x∃Yp(x, y).b. ∀y∃xP(x, y).c. ∃x∀yP(x, y).d. ∃y∀xP(x, y).A general state space search algorithm is implemented in search.py. Go through this and try to understand it. An example of how to implement a particular search problem using the state space code is shown in pitcher.py. Note in particular how the PitcherState class works in conjunction with the Search class. Using the PitcherState class as a model, write a Simpsons class that implements a solution to the following slightly modified problem from an episode of the Simpsons called Gone Maggie Gone from 2009. Maybe you remember it. Homer Simpson has to move his daughter Maggie, his dog Santa's Little Helper, and a jar of medical marijuana that looks like candy across a river. He can only take one item in his boat at a time. He can't leave Maggie alone with the medical marijuana (or she will eat it) and he can't leave Santa's Little Helper alone with Maggie (because the dog will pester the girl). Formulate the actions for this problem and implement them. Be careful to ensure that illegal…