Suppose that: • variables X and Y can represent any vertices in a graph G, • the predicate adjacent(X, Y) is true if and only if X and Y are adjacent in G. Write a statement in predicate logic with the following meaning: "Some vertex in G has no neighbours." The following symbols are provided for you to copy if you wish (though not many of them a needed in this question, and you are not limited to using only the symbols that are listed here): 3 V ^v - Answer:
Q: QUESTION 5 Describe the language produced by the following recursive set definition (assume . = {0,…
A: Theory of Computation Question. Answer given in next section.
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Q: QUESTION 5 Describe the language produced by the following recursive set definition (assume -{0,1}…
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Q: 1.All animals are dogs. 3.Some animals are not cats. 4.Every animal that is a dog is not a cat.
A: 1.All animals are dogs. 3.Some animals are not cats. 4.Every animal that is a dog is not a cat.
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- AI a modern approach 10.3 The monkey-and-bananas problem is faced by a monkey in a laboratory with some bananas hanging out of reach from the ceiling. A box is available that will enable the monkey to reach the bananas if he climbs on it. Initially, the monkey is at A, the bananas at B, and the box at C. The monkey and box have height Low, but if the monkey climbs onto the box he will have height High, the same as the bananas. The actions available to the monkey include Go from one place to another, Push an object from one place to another, ClimbUp onto or ClimbDown from an object, and Grasp or Ungrasp an object. The result of a Grasp is that the monkey holds the object if the monkey and object are in the same place at the same height. a. Write down the initial state description.b. Write the six action schemas.c. Suppose the monkey wants to fool the scientists, who are off to tea, by grabbing the bananas, but leaving the box in its original place. Write this as a general goal (i.e.,…QUESTION THREEConsider the thirsty person problem given below: To drink, a thirsty person must have three things; water, ice and a glass. There are three thirsty people, each having a different one (and only one) of the three required items. A fourth person, a server has unlimited supply of all three items. If nobody is drinking, the server places two of the three items (chosen at random) onto table. Thirsty person who can make a drink from those two items will pick them up and drink a glass of ice water. When done, thirsty person will notify the server and the process will repeat. Write a process that will control the thirsty person and the server using semaphores. (i) What is a critical section in code?Explain the three properties that any solution to the Critical Section Problem should guarantee.Explain the role the Operating System plays in Garbage-In-Garbage-Out (GIGO).For this problem, the domain is the set of all solar system objects: P(r) means r is a Planet M(r) means r is a Moon O(1, y) means r orbits y Formulate the following statements using predicate logic. You may use x + y to indicate that the x and y are different. 1. All plancts orbit the sun and all moons orbit a planet. 2. Some planets have no moon. 3. Some planets have two or more moons. 4. Some objects orbit the sun that are not plancts 5. Everything that orbits the sun is a planet. (Also prove that this statement is the negation of the previous statement) 6. Pluto is a planct! 1
- LetC(x)be the statement "xhas a cat",D(x)"xhas a dog", andH(x)"xhas a horse". LetUbe the set of all students in your class. Express each of the following statements in terms ofC(x),D(x),H(x), quantifiers, and logical connectives. a. A student in your class has a cat, a dog, and a horse. b. Some student in your class has a cat, a dog, but not a horse. c. No student in the class has a cat, a dog, and a horse. Please give proper explanation and typed answer only.The landline telephone numbers in a country typically consists of an area code (prefix) followed by the subscriber number. Meaning, a telephone number typically has a . To call a subscriber we just need to call the number with the relevant prefix followed by the subscriber number. The 'United Planets' is a federation of planets that has a Telephone Company called 'Astronomy Telecom' which uses the following classification or scheme for telephone numbers similar to our landline telephone numbers in a country. Stars: Starts with 511 followed by subscriber number (consider there are infinite stars where each star is considered as a subscriber). Comet: Starts with 522 followed by subscriber number (consider there are infinite comets where each comet is considered as a subscriber). Asteroid: Starts with 533 followed by subscriber number (consider there are infinite asteroids where each asteroid is considered as a subscriber). Planets: Starts with 12, followed by at least 6 digits and none…Regular expression to NFA to DFA conversion: Describes the process of taking a unique regular expression, converting that regular expression to an NFA, then converting the NFA into a DFA. Your regular expression must have at minimum two union, two concatenation, and two Kleene star operations. As followed, concatenations of single charaters can be condensed. Your regular expression cannot be a solved problem from any book. You should describe the regular expression with both processes to convert the regular expression to an NFA and the conversion of that NFA into a DFA.
- Loop invariants Consider the following code, assuming that i, x, y, and n are integers, with n > 0. • State a non-trivial loop invariant for variable x. • Prove the loop invariant. Be sure that the proof includes the final conditions after the loop has ended. Note: a correct proof of an incorrect invariant will still receive partial credit. • Give the final value of a in terms of n. Hint: is the pattern close to (e.g. off by one) from some other pattern you might recognize? Hint: you might need to include a condition for y somewhere within your proof. i = 0; x = 1; while in do y = x + 2; x=x*y; i = 1 + 1; After the loop, x = (the invariant goes here)Let l(x) be "x has an internet conection" and C(x, y) be "x and y have chatted over the internet". Assume the domain is all students in a class. Express the following using quantifiers. 1. Jerry does not have an internet connection 2. Exactly one student in the class has an internet connection 3. Someone in your class has an internet connection but has not chatted with anyone else in the class.Can you help me with this code because I am struggling. The Lights Out puzzle consists of an m x n grid of lights, each of which has two states: on and off. The goal of the puzzle is to turn all the lights off, with the caveat that whenever a light is toggled, its neighbors above, below, to the left, and to the right will be toggled as well. If a light along the edge of the board is toggled, then fewer than four other lights will be affected, as the missing neighbors will beignored. In this section, you will investigate the behavior of Lights Out puzzles of various sizes by implementing a LightsOutPuzzle class. Once you have completed the problems in this section, you can test your code in an interactive setting using the provided GUI. See the end of the section for more details. Task: A natural representation for this puzzle is a two-dimensional list of Boolean values, where True corresponds to the on state and False corresponds to the off state. In the LightsOutPuzzle class, write an…
- tonquage accepting any no.fa's } prite a P.E for the and b's over, & = {a,b?A hungry mouse wants to eat all four fruits in a maze such as the one below, in as few moves as possible.. At each turn the mouse can move any number of squares in one of the directions up, down, left or right, but it is not allowed to enter (or jump over) any walls (i.e., the black squares). Thus, the mouse moves just like a rook in chess. To eat a fruit, the mouse has to stop at that square. Assume that the maze has 4 fruits, and the size of b xh squares. 1. Give a suitable representatión of the states in this searching problem. 2. How many possible actions can the mouse perform at each move? (1.e., what is the branching factor?)4. Remove the left recursion from the following production rule to obtain a new rule: A = A '0' | '1' | A '2' | '3' | A '4' | '5'