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- 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! 1PLEASE TYPE ANSWE*** Exercise 1.7.4: Translating quantified statements from English to logic, part 3. In the following question, the domain is a set of employees who work at a company. Ingrid is one of the employees at the company. Define the following predicates: S(x): x was sick yesterday W(x): x went to work yesterday V(x): x was on vacation yesterday Translate the following English statements into a logical expression with the same meaning. (g) Someone who missed work was neither sick nor on vacation. (h) Each person missed work only if they were sick or on vacation (or both). (i) Ingrid was sick yesterday but she went to work anyway.Premise 1: All the cups in my house are green. Premise 2: I am drinking from a green cup. Conclusion: I must be at home. Decide whether the above argument is inductive or deductive. If the above argument is inductive, decide if it is strong or weak. Select not applicable if the argument is deductive. If the above argument is deductive, decide if it is valid or invalid. Select not applicable if the argument is inductive.
- Please solve quicklyDefine the following predicates: • A(x) : x is on the board of directors." • E(x) : x earns more than $100, 000. • W(x) : x works more than 60 hours per week. The domain is the set of all employees of a certain company. Match each English statement with its equivalent logical expression. ? v 1. Everyone who works more than 60 hours per week earns more than $100,000. A. 3x(E(x) ^ ¬W(x)) B. Vx(W(x) → E(x)) C. Ex(¬A(x) → E(x)) D. Vx(W(x) ^ E(x)) E. 3x(¬A(x) ^ E(x)) F. 3x(A(x) ^ ¬E(x)^ W(x)) G. Ex(A(x) V ¬E(x) V W(x)) H. Vx(A(x) → E(x)) I. Vx(A(x) ^ E(x)) 2 v 2. Someone on the board of directors does not earn more that $100.000 and works more than 60 hours per week. ? v 3. Every member of the board of directors earns more than $100,000. 2. v 4. There is someone who is not on the board of directors and earns more than $100,000. ? v 5. There is someone who earns more than $100,000, but does not work more than 60 hours per week.What's the set of free variables in the following lambda-calculus term? (lambda x. lambda y. y x) z (lambda x. x y)
- For each of the following expressions, write functions f1, f2, f3, and f4 such that the evaluation of each expression succeeds, without causing an error. Be sure to use lambdas in your function definition instead of nested def statements. Each function should have a one line solution. f1 takes in nothing and returns 3. f2 takes in nothing and returns a function that takes in nothing and returns 3. f3 takes in nothing and returns a function that takes in 1 value and returns that same value. f4 takes in nothing and returns a function. This function takes in nothing and returns another function. This next function takes in a value and returns yet another function. This final function takes in nothing and returns the value passed into the previous function (if this explanation is confusing, have a look at the doctest, and it might be more clear). def f1(): >>> f1() 3 |||||| "*** YOUR CODE HERE ***" def f2(): |||||| >>> f2() () 3 |||||| "*** YOUR CODE HERE ***" def f3(): |||||| >>> f3() (3)…When a Predicate has only a single Clause, which of the following Clause coverage criteria is enough to cover the Clause. a. General Inactive Clause Coverage b. Restricted Active Clause Coverage c. General Active Clause Coverage d. Predicate Coverage e. Combinatorial Clause CoverageOne of the following items is a run-on (or fused) sentence, another contains a comma splice, and another is correct. Choose the item that is correct. One of the following items is a run-on (or fused) sentence, another contains a comma splice, and another is correct. Choose the item that is correct. The food in that diner is awful besides the service is slow. The food in that diner is awful, besides the service is slow. The food in that diner is awful; besides, the service is slow.
- What does it mean that the object function is more relevant than the restrictions when dealing with linear programming issues?ONLY ANSWERS FOR D E AND FLet P(x) be the statement "x can speak English", Q(x) be the statement "x knows the computer language C++" and R(x) be the statement "x is a good programmer". Express the following clause in terms of P(x), Q(x) R(x), quantifiers, and logical connectives. The domain for quantifiers consists of all students at your school. "There is a student at your school if he knows C++ and he cannot speak English then he knows C++ or he cannot speak English if and only if he is a good programmer."