Given the following vocabulary: smart(x): x is a person; x is smart student(x): x is a student at(x, y): x is a person, y is a school; x is a school y
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- Predicate calculus, converting from english to logic. Let H(p,d) be the predicate to person (p) has dog (d) 1. Not all people have dogs 2. There's a person that does not have every dog 3. There's a person who has a dog 4. There's a person who doesn't have a dog 5. All people have a dog 6. There's no dog that a person doesn't have 7. All people have all dogsConvert it into predicate logic: Every student in the class has either visited Canada or Mexico.Predicates S(x): x is a studentD(x): x is a petH(x): x is a homeT(x, y): x is owned by y (y owns x)E(x, y): x eats at yK(x, y): x knows yL(x, y): x and y play together [Q2: Translate sentence to logic] Some pet plays with every student. Answer: [Q3: Translate sentence to logic] If a pet plays with a student at some home, then it eats at this home. Answer: [Q4: Translate formula to English] ∀x(S(x) → ∃y(D(x) ∧ L(x,y))) Answer: [Q5: Invent a Problem ] Answer:
- Represent the following facts in predicate logic: The last meeting of the club was at Joe’s house. John likes all kinds of foods. Also proves that John likes peanuts using backward chaining and considering following statements: John likes all kinds of food. Apples are food. Chicken is food. Anything anyone eats and isn’t killed by is food. Bill eats peanuts and is still alive. Sue eats everything bill eats.Computer Science The knowledge of an expert system is given as follow: male(john).male(sam).male(peter).male(david).female(mary).female(betty).female(jane).female(sarah). a). A new predicate, likes, with two arguments (i.e. likes(male,female)), is required to represent the likes relationship of all possible male and female. Using variable(s), write the rule(s) that can generate the required knowledge.b). Using variable(s), write the rule(s) that can also provide the knowledge, likes(female,male).c). Given that sam and mary are sibling, the likes relationship between sam and mary should be omitted from the knowledge. Modify the rule(s) defined above.Use the predicate symbols shown. Everyone with red hair has freckles. Someone has red hair and big feet. Everybody who doesn’t have green eyes doesn’t have big feet. Therefore someone has green eyes and freckles. R(x), F(x), B(x), G(x)
- Four mathematicians have a conversation, as follows: ALICE: I am insane. BOB: I am pure. CHARLES: I am applied. DOROTHY: I am sane. ALICE: Charles is pure. BOB: Dorothy is insane. CHARLES: Bob is applied. DOROTHY: Charles is sane. You are also given the following information: Pure mathematicians tell the truth about their beliefs. Applied mathematicians lie about their beliefs. Sane mathematicians' beliefs are correct. Insane mathematicians' beliefs are incorrect. With the preceding clues, classify the four mathematicians as applied or pure, and insane or sane. Briefly explain your logic.i. Marcus was a man. ii. All man are person.iii. Marcus was a Pompeian. iv. All Pompeians were Romans.v. Caesar was a ruler. vi. All Pompeians were either loyal to Caesar or hated him.vii. Everyone is loyal to someone. viii. People only try to assassinate rulers they are not loyal to. ix. Marcus tried to assassinate Caesar. Convert the following sentences into first order logic. And analyzing the above sentence answer and reason “Was Marcus loyal to Caesar?”1. Translate the following into Predicate Logic. Do not forget to add the translation key andall necessary information.a) Exactly two people are lying.b) If someone eats the cake, then they can’t be Stacy.c) I know only one person who’s that lucky
- Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.) A(x): x is an animal B(x): x is a bear H(x): x is hungry W(x): x is a wolf a. Bears are animals. b. No wolf is a bear. c. Only bears are hungry. d. If all wolves are hungry, so are bears. e. Some animals are hungry bears. f. Bears are hungry but some wolves are not. g. If wolves and bears are hungry, so are all animals. h. Some wolves are hungry but not every animal is hungry.Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.)L(x): x is a lionR(x): x roarsP(x): x is a predatorZ(x): x is a zebraE(x, y): x eats ya. All lions are predators.b. Some lions roar.c. Only lions roar.d. Some lions eat all zebras.e. All lions eat all zebras.You are given the predicates Friend(x.y) which is true is x and y are friends and Personx) TRUE is x is a person. Use them to translate the following sentences into first-order logic Every person has a friend. My friend's friends are my friends. translate the following from first order logic into english Vx vy 3z Person(x) A Personty) A Person(z) A Friend(x,2)A Friend(y a) x By Person(x)- [Dayy) A Badly))