Let F(x,y): "x is friend with y", N(x): "x is funny", W(x): "x is wise",R(x): "x is fair". The domain for x and y is the set of all persons.Select the symbolic (s) of the following sentence:"All not fair persons are friends with all funny persons"U vxVy ¬R(x) ^ N(y) →F(x,y)O vx Vy (R(x) v ¬N(y)) v F(x,y)O vxVy ¬F(x,y) →R(x) v ¬N(y)O None of all the proosed answersO ax Vv R(X) v ¬NCV)→F(x.V)

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Answered: Let F(x,y): "x is friend with y", N(x):…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Q7: Translate the following statement into English, where R(x) is "x is a rabbit" and H (x) is "x hops" and the domain consists of all animals. • 3x(R(x) → H (x)) Q8: Translate in two ways the following statement into logical expressions using predicates, quantifiers, and logical connectives. First, let the domain consist of the students in your class and second, let it consist of all people. Everyone in your class has a cellular phone. Q9: (* Let P (x, y) be the statement "Student x has taken class y," where the domain for x consists of all students in your class and for y consists of all computer science courses at your school. Express the following quantification in English. 3XVYP (x, y)
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Express this in predicate logic: Each email address has exactly one email box. M(x): x is an email address B(x,y): x has an email box y
Given the domains m e MOVIES and ce CHARACTERS and the following predicates: • sW(m): m is a Star Wars movie. A(c, m): c is a character who appears in the movie m • D(c): c is a Droid. • L(m): I liked m. • Q(c, q): c says q (e is quoted as saying q.) • jarjar is the character Jar Jar Binks • bad is the quote: "I've got a bad feeling about this!"
21. Let the following predicates be given. The domain is all computer science classes. I(r) = "x is interesting." U(x) = "x is useful." H(x, y) = “x is harder than y." M(x, y) = “x has more students than y." (a) Write the following statements in predicate logic. i. All interesting CS classes are useful. ii. There are some useful CS classes that are not interesting. iii. Every interesting CS class has more students than any non- interesting CS class. (b) Write the following predicate logic statement in everyday English. Don't just give a word-for-word translation; your sentence should make sense. (3)[I(x) A (Vy)(H(x,y)→ M(y, x))] (c) Formally negate the statement from part (b). Simplify your negation so that no quantifier lies within the scope of a negation. State which derivation rules you are using. (d) Give a translation of your negated statement in everyday English.
Need #2 please help
4. Let P be "It is humid" and let Q be "sum of 9 and 11 is 21". Give a simple verbal sentence which describes each of the following statements: (a) ¬Q, (b) P V Q, (c) (¬P) ^ Q, (d) (¬P) V (–¬Q).
Determine, using semantic tableaux whether the following logical consequence is valid or not: (pVavr) pVrv -sv (gA s)-
This proposition is a tautology: ((p→¬q)∧q)→¬p True or false I would appreciate step by step explanation
A student club holds a meeting. The predicate M(x) denotes whether person x came to the meeting on time. The predicate O(x) refers to whether person x is an officer of the club. The predicate D(x) indicates whether person x has paid his or her club dues. The domain is the set of all members of the club. The names of the members and their truth values for each of the predicates is given in the following table. Indicate whether each expression is true or false. If a universal statement is not true, give a counterexample. If an existential statement is true, give an example. Name M(x) O(x) D(X) Hillary T F Bernie F F Donald F F Jeb F Carly F F Ex (M(x) A D(x)
2. Let P(x) be "x is a student in this class," Q(x) be “x knows how to write programs in Python," and R(x) be “x can get a good job," where the domain of x consists of all people. Write the following argument in argument form and use the rules of inference to show that the argument is valid. Tom is a student in this class. Tom knows how to write programs in Python. Everyone who knows how to write programs in Python can get a good job. Therefore, some student in this class can get a good job.

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