5.3 Find a match in the following instance of the Post Correspondence Problem. ab aba abab b a
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- 8) Let O be the set of odd numbers and O’ = {1, 5, 9, 13, 17, ...} be its subset. Definethe bijections, f and g as:f : O 6 O’, f(d) = 2d - 1, d 0 O.g : ø 6 O, g(n) = 2n + 1, n 0 ø.Using only the concept of function composition, can there be a bijective map from øto O’? If so, compute it. If not, explain in details why not...................................................................................................................................... [2+8]b) A Sesotho word cannot begin with of the following letters of alphabet: D, G, V, W,X, Y and Z.We define the relation: A Sesotho word x is related to another Sesotho word y if xbegins with the same letter as y.Determine whether or not this is an equivalence relation.If it is an equivalence relation then1. Compute C(sekatana)2. How many equivalence classes are there in all, and why?3. What is the partition of the English words under this relation?If it is NOT an equivalence relation then explain in details why it is notIs A a subset of B if; A = { 9, 8, 7, 6, 5} B ={ 5,6, 7, 8, 9}
- Quick Answer PleaseCorrect answer will be upvoted else downvoted. Computer science. Positive integer x is called divisor of positive integer y, in case y is distinguishable by x without remaining portion. For instance, 1 is a divisor of 7 and 3 isn't divisor of 8. We gave you an integer d and requested that you track down the littlest positive integer a, to such an extent that a has no less than 4 divisors; contrast between any two divisors of an is essentially d. Input The primary line contains a solitary integer t (1≤t≤3000) — the number of experiments. The primary line of each experiment contains a solitary integer d (1≤d≤10000). Output For each experiment print one integer a — the response for this experiment.Q2.2 Derivative of Softmax function Implement a function Dsoftmax(z) such that caluclate the gradient of softmax function. Verify it with several examples.
- Additional information: r(x) is the open statement "x>0". The universe is integers.(a) Give an algorithm for computing the intersection of a 3D triangle abc with a sphere with center o and radius r. The result is a polygon or the empty set. (b) Give an algorithm for computing the intersection of a 3D triangle abc with a ray based at o with direction u. Handle the cases where the result is a point or empty. What case are you not handling?EXERCISE 6.4 Define the binary ↑ (Sheffer's stroke), and its dual as follows: x ↑ y10 :y x: 101 011 x + y10 : y 100 00 1 Show that {t} is expressively complete, and that so is {4}. (Hint: Express some expressively complete set using the connective.)
- Q2: Search a problem consists of four juice bottles A, B, C, and D (Sol, Moon, Costa, and Dad). They can be arranged in any order from left to right, except that bottle A can never be further to the right than bottle D. For example, ABCD, CBAD, and CADB is possible states of our world, whereas DCBA, CDAB, or BCDA can never occur. The world can be manipulated by the schema swap(x, y), which swaps the bottles in positions x and y. For example, swap (1, 2) turns state BCAD into CBAD. Assume that your world is in the state ADBC, but you would like it to be in state CBAD. Draw the search tree Solve the problem by greedy if the estimated value is the # of bottles in an incorrect position. Solve the problem by A* search if f'(n) = # of operations performed + (min # of moves of the bottles to be in its position. Propose 5 chromosomes as an initial population from the basics of the problem, and apply GAs if the fitness is the # of bottles in incorrect position * of infeasible solutions, use 1…3. Write findMaxR(self, root) that will return the maximum of a BST using recursion. 4. Write find MinR(self, root) that will return the minimum of a BST using recursion.B1 Write a function NearestPoint (G,v,mylist) which takes as input a networkx object G representing a weighted graph, an object v which will be a node of G, and a list mylist of some other nodes of G. The function should return whichever node in mylist is nearest to v (in the sense of the minimum weight path from v). In the event of a tie, it should return the nearest node which appears earliest in mylist. CORDELIA WEBB UNIVERSITY OF LEEDS, 2023/24 B2 We say that a weighted graph has the Unique Weight Prop- erty (UWP) if no two edges have the same weight. Recall from Workshop 9-10 that if G is connected and has the UWP then it will automatically have a unique spanning tree. Write a func- tion UWP (G) which tests whether or not G has the UWP and returns True or False accordingly. Hint: extract a list of edge-weights and use the count func- tion to see how many times each appears. B3 Write a function GoodPath (G,a,b) which takes as input a net- workx object G representing a connected…