Questions_PM2

Below are some predicates and their corresponding statements:    p(x): x is a student in your class  q(x): x has taken a course in logic programming Here, the domain for quantifiers consists of all people. Choose the correct proposition for the sentence:  All student in your class has not taken a course in logic programming.   a.  ∀x¬(P(x) → Q(x)) b. ∀x(P(x) → ¬Q(x) c. ¬∀x (P(x) → Q(x))  d. ¬∃x(P(x) ∧ Q(x))

Suppose P and Q are the statements: P: Jack passed math. Q: Jill passed math. (a) Translate “Jack and Jill both passed math” into symbols. (b) Translate “If Jack passed math, then Jill did not” into symbols. (c) Translate “P ∨ Q” into English. (d) Translate “¬(P ∧ Q) → Q” into English.

1. Teachers in the Middle Ages supposedly tested the real-time propositional logic ability of a student via a technique known as an obligato game. In an obligato game, a number of rounds is set and in each round the teacher gives the student successive assertions that the student must either accept or reject as they are given. When the student accepts an assertion, it is added as a commitment; when the student rejects an assertion its negation is added as a commitment. The student passes the test if the consistency of all commitments is maintained throughout the test. a.)  Suppose that in a three-round obligato game, the teacher first gives the student the proposition p → q, then the proposition ¬(p ∨ r) ∨ q, and finally the proposition q. For which of the eight possible sequences of three answers will the student pass the test? b.)  Explain why every obligato game has a winning strategy.

Write the following English statements using the following predicates and any needed quantifier. The domain of all variables are all at the school  S(x): x is a student F(x): is a faculty member A(x, y): x has asked y a question   Every student has asked Dr. Lee a question

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.

Sentential Logic Translation (It is mandatory to use the Letters given in the following questions; do NOT choose other Letters): If neither inflation (I) nor unemployment (U) continues at their current low rates, then there will be recession (R) if and only if stock prices (S) do not drop dramatically and either heating oil (H) or gasoline prices (G) continues to rise. Any ONE (i.e., only ONE) of my three children [Peter, John, Mary] is telling the truth. (P, J, M)

13. p(x): x is intelligent  q(x): x reads book r(x): x is a student in your class Find the correct English translation for the following logical expression: ∀x(r(x)→(p(x) Λ q(x)) a. None b. There is an intelligent student in your class who reads book c. Every student in your class is intelligent and reads book d. All student in your class is intelligent and doesn't read book

A propositional logic expression is in full disjunctive normal form if it is a disjunction (i.e., a term that uses only the 'OR' operator) of one or more conjunctions (i.e., terms that uses only the 'AND' operator), and each of the variables in the expression appears once (and only once) in each conjunction. Using this definition, what is the full disjunctive normal form of the expression below? (¬((P V (¬R)) → (¬Q))) Select one: (¬P AQA¬R) V (PA¬Q A ¬R) V (PAQA¬R) (¬P ^¬QA¬R) V (¬P ^ Q ^ ¬R) V (P ^ Q A R) (¬P A¬QA ¬R) V (¬P AQA¬R) V (PAQA¬R) O none of these options (¬P AQA¬R) V (PAQA¬R) V (PAQA R) (¬P AQA ¬R) V (¬P ^QA R) V (P AQA R)

Consider the following argument: No good car is cheap. A Simbaru is not cheap. .: A Simbaru is a good car. A. Give a representation of the argument using predicate/quantified logic. B. Determine whether the argument is valid or invalid by constructing a simple logic version of the argument that is specific to Simbaru, and prove it via a truth table. C. Give a representation of the argument using set logic. D. Determine whether the argument is valid or invalid using diagrams.

2. For the following wffs, indicate which variables are free and which are bound (you can use 'F' for free and 'B' for bound.) Either (i) draw a vertical line underneath each variable with the letters 'F' or 'B' at the bottom of each vertical line or (ii) color the bound variables red and the free variables green. Make sure you know which symbols are variables. Not every symbol in the language of predicate logic is a variable. The reading (Scope, binding, and quantifier expansions) lists the symbols that are variables and the symbols that are names of objects (i.e., individual constants). Names of objects are not variables. You can also write the wffs on a piece of paper and submit a photo of it. (a) (Ex) (y) (z) ((Ayz --> Bzzy) v (Fxac --> Hzzu)) (b) (х) (у) Нууу --> (2) (Fzy v Hxх) (c) (Ez) (x) (у) (Ахyzbbw v Bxуcdvz)

Suppose that p and q are statements so that  p → q  is false. Find the truth values of each of the following. (a) ~p → q TrueFalse     (b) p ∨ q TrueFalse     (c) q → p TrueFalse

Q: The propositional variables b, v, and s represent the propositions: b: Alice rode her bike today. v: Alice overslept today. s: It is sunny today. Select the logical expression that represents the statement: “Alice rode her bike today only if it was sunny today and she did not oversleep.”  b→(s→¬v)     2. b→(s∧¬v)   3. s∧(¬v→b) 4.  (s∧¬v)→b Group of answer choices b→(s∧¬v) b→(s→¬v) s∧(¬v→b) (s∧¬v)→b   2);  The following two statements are logically equivalent   (p → q) ∧ (r → q) and (p ∧ r) → q Group of answer choices True False

Q: The propositional variables b, v, and s represent the propositions:   b: Alice rode her bike today. v: Alice overslept today. s: It is sunny today.   Select the logical expression that represents the statement: “Alice rode her bike today only if it was sunny today and she did not oversleep.”  b→(s→¬v)     2. b→(s∧¬v)   3. s∧(¬v→b) 4.  (s∧¬v)→b     Group of answer choices   A): b→(s∧¬v) B): b→(s→¬v) C): s∧(¬v→b) D): (s∧¬v)→b

Write the following English statements using the following predicates and any needed quantifier. The domain of all variables are all people associated in a university    S(x): x is a student F(x): is a faculty member A(x, y): x has asked y a question There are at least two students who have asked every faculty member a question There is a faculty member who has asked every other faculty member a question

Let p, q, and r represent the following statements: p:  The first ball is red. q:  The second ball is white. r:  The third ball is blue. Which would be the correct English statement for the symbolic form (¬¬p ∧∧ q) →→ r ? Group of answer choices A .If the first ball is red or the second ball is white, then the third ball is blue. B. If the first ball is not red or the second ball is white, then the third ball is blue. C .If the first ball is not red and the second ball is white, then the third ball is blue. D. If the first ball is red and the second ball is white, then the third ball is blue.

Convert each of the following argu- ments into formal statements, e.g., define sentences existentially and/or universally quantified statements. Then determine which rules of logic have been applied and explain whether or not they have been ap- plied correctly. if you do the homework you will pass the final. Somebody did not pass the final. Therefore somebody did not not do the homework. If you do the homework you will pass the final. Curly did not do the homework. Therefore Curly will not pass the final. If you don’t do the homework, you won’t pass the final. Moe did the homework. Therefore Moe passed the final.

Logic is used in formal methods. Conceptually, propositional and predicate logic are the most common types of logic.    A first-year student in discrete mathematics wants to use propositional and conditional logics to test software. Assist this kid.    One idea is to talk about what's good and bad about reasoning and software testing. How should testing of formal programmes be done? Which reason is the best?

Translate the English sentence to propositional logic. a) Every student majoring in Cumputer science need to visit the science museum b) Use the De Morgan’s law to find the negation of “Some students has visited the science museum.”

Use prolog for the coding Using prolog write a predicate to guess a number interactively from 1 to 100 in at most 4 tries. Output can be obtained with predicates write(X) and nl, and input with predicate read(X) (integer input will be followed by a “.”). The secret number can be hardcoded.

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?”

Construct proof for the following argument within the system of sentential logic: 1. ~(~D ⊃ ~C) ⊃ ~B            Premise2. ~B ⊃ A                            Premise3. (Y V C) & (~C V ~A)     Premise    /: . D V (A V Y)

Using the predicate symbols shown and the appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.) D(x): x is a day S(x): x is sunny R(x): x is rainy M: Monday T: Tuesday All days are sunny.  which of these answers are right? a. (∀x)[D(x) ∧ S(x)] b. (∀x)[D(x) → S(x)] c. (∃x)[D(x) ∧ S(x)] d. (∃x)[D(x) → S(x)

Let K (x, y) be the statement "x knows y", where the universe of discourse for both x and y is the set of all people. (Assume it is possible for x to know y while y does not know x, and hence K(x, y) and K(y,x) are different statements.) Translate the sentence "there are two distinct persons who know each other, and no one else" into First Order Logic. 2.

For each of the following statements about regular expressions α, β and languages A, B, state whether they are true or false. Provide a one-sentence justification for each answer.